Wave transmission line

Abstract

The invention relates to a wave transmission line (1) comprising a printed circuit structure (10) extending in a transmission direction (D) of the transmission line, the printed circuit structure (10) comprising, on one face, a metal layer (15) forming a ground plane, the printed circuit structure (10) having metallized lateral vias (20) made through it which are electrically connected to the metal layer (15) and arranged on either side of a general symmetry plane (P) of the transmission line (1) including the transmission direction (D), the transmission line (1) further comprising an electrically conductive plate (50) and an adhesive structure (40, 41) which spaces and electrically insulates the electrically conductive plate (50) from the face (17) of the printed circuit structure opposite the metal layer (15). The adhesive structure (40, 41) is thinned and debonded from the printed circuit structure, or even interrupted, in line with the general symmetry plane (P), leaving a free space (45) extending in the transmission direction (D) between the printed circuit structure (10) and the electrically conductive plate (50) for the propagation of waves through air or vacuum.

Description

[0001] Description

[0002] Title: Wave transmission line

[0003] An electromagnetic signal transmission line and a method of manufacturing the same are provided.

[0004] It falls within the field of high-frequency communications, and more specifically, microwaves. Microwave waves are electromagnetic waves that propagate in air, vacuum, or dielectric materials, and have a wavelength that can be of the order of a millimeter, a centimeter, a decimeter, or several decimeters, without exceeding 1 m.

[0005] They are used with specific electronic circuits, as well as antennas, sensors, and other specific electronic components. In these applications, the waves transmit an analog signal.

[0006] Propagation induces signal intensity losses, which are higher when the signal is transmitted over distances that are significant compared to the signal wavelength - they are therefore quantified in terms of linear losses. The design of transmission lines seeks to minimize these linear losses, particularly in a context where antenna array equipment is installed.

[0007] Transmission lines of the rectangular metal waveguide category are known, with propagation in air or vacuum and correspondingly low losses, but which are relatively bulky - in this case it is necessary for the width of the waveguide to be greater than half the wavelength to be transmitted, which is a lot, especially below 10 GHz, and quite expensive.

[0008] Transmission lines are also known in the coaxial cable category, with a solid dielectric material forming a sheath between a central conductor cable and a conductive cylinder at the periphery. Also known are lines on printed circuits, forming planar structures often with a ground plane, with conductive lines in the form of track, slot, ribbon, coplanar guides or microstrip, which allow propagation in a planar solid dielectric material interposed according to various geometries between lines of electrically conductive metallic materials. These solutions are compact, but suffer, at equal transmission distance, from high signal intensity losses because the wave circulates in the dielectric substrate.

[0009] Solutions to find a compromise between size and losses are known by which a central metallic rib (ridge in English) is placed in a transmission line propagating in air or vacuum, which leads to a structure called a ridge waveguide, which allows the size of the rectangular waveguide to be reduced, but nevertheless develops significant losses, and may require complex and therefore expensive machining.

[0010] Finally, waveguides are known that are made on printed circuits, and that take the form of a dielectric substrate between two electrically conductive planes and on each side a line of periodic metallized holes or slots electrically connecting these two conductive planes, to confine the wave in a central part forming the guide. These structures are known by the acronym SIW (for Substrate Integrated Waveguide), and they exist with or without an additional central metal rib. The manufacturing is based on a single-layer printed circuit with its two metallized surfaces, and is therefore simple, but there are losses due to the dielectric constituting the propagation zone.

[0011] We know from Mohammadi and Demir Progress in electromagnetics C, 46, 125, 2014 "loss reduction in substrate integrated waveguide structure", in a dielectric substrate, a mixed dielectric and air transmission line, between two conductive planes, and rows of metal vias of large diameters and close to each other in the dielectric substrate. The structure is formed by a superposition of three layers: a thick layer of copper, a layer of dielectric (a single-layer printed circuit) surrounded by two thin layers of copper and cut in central section in the direction of the propagation line, a row of vias being held on each side of the cut, then again a thick layer of copper. The three layers are screwed to each other by screws forming two rows placed parallel to the rows of vias, towards the outside, and with a spacing between the screws much wider than between the vias.The cavity formed is therefore delimited by two copper surfaces at the top and bottom, as well as two side walls of dielectrics behind which are two rows of vias: one on the left and one on the right. And the structure is therefore very thick, given the need to place thick copper sheets on either side of the printed circuit cut from side to side.

[0012] We also know solutions by assembling, between two metal plates which remain isolated from each other, periodic structures of several rows of metal pads mounted on one of the plates on either side of a central zone comprising a central rib of conductive material again called ridge (and the structure is then called a ridge gap waveguide RGW) or alternatively a central void filled with air (and the structure is called a groove gap waveguide GGW), the wave propagating between the rows of pads, confined due to the periodic structure of these rows on either side of its path, also taking into account its wavelength which belongs to a range of wavelengths stopped by the periodic structure (the rows of pads form a band gap structure - EBG for electromagentic band gap).The structure is advantageous due to the absence of an electrical connection between the two metal plates, which allows for assembly without contact constraints (few or no screws, no welding, etc.). But this solution is generally complicated to implement at the stage of machining the individual parts.

[0013] We know from Oyedokun et al. Proceedings of the 47th European microwave conference Oct. 2017 "Experimental characterization of planar groove gap waveguide and cavity" a structure based on a multilayer printed circuit with periodic assembly of blind vias on either side of a volume of dielectric material. The assembly is formed by a superposition of three planar structures, with two conductive planes on either side. It is formed by lamination of two substrates including towards the outside only metallic planes (laminates), and between the two layers, a dielectric prepreg (prepreg), that is to say a layer of dielectric without metal. Once the pads of a GGW or an RGW are assimilated to the metallized vias of this construction, we find the structures of a GGW or an RGW, with a bandgap structure but also a simpler manufacturing, since based on printed circuit products.On the other hand, there is a complete filling of the wave path by dielectric, which induces more losses.

[0014] Thus, in view of this prior art, we are faced with a problem of significant losses as soon as miniaturization efforts are made.

[0015] To solve this problem, a wave transmission line is proposed comprising, as in Oyedokun et al., a printed circuit structure extending in a transmission direction of the transmission line, the printed circuit structure comprising on one face an electrically conductive metal layer forming a ground plane, the printed circuit structure being pierced with metallized lateral vias electrically connected to said metal layer and arranged on either side of a general plane of symmetry of the transmission line including the transmission direction, said lateral vias contributing for said transmission line to an electromagnetic band gap structure, the transmission line further comprising an electrically conductive plate and a bonding structure, spacing and electrically insulating an essentially planar face of said electrically conductive plate from an essentially planar face of the printed circuit structure opposite the metal layer forming a ground plane.Flat surfaces are understood to be flat subject to the presence of local concavities.

[0016] But in addition, the structure of the invention has the original characteristics according to which the adhesive structure is thinned, or even interrupted, at the level of the general plane of symmetry, leaving a free volume extending in the transmission direction between the printed circuit structure and the electrically conductive plate for the propagation of waves in air, a gas or a vacuum.

[0017] Thanks to this feature, low linear losses are obtained since the wave propagates at least partly in air, a gas or a vacuum, and yet we are able to take advantage of an electromagnetic bandgap structure in a printed circuit, which is easy to manufacture and can be done in a very space-saving manner.

[0018] Optionally and advantageously, the following features may be included in the wave transmission line: the sticky insulating structure may be a single layer of double-sided adhesive material, perforated around the plane of general symmetry or thinned by the presence of a flat around the same plane, the flat being preferably placed on the side of the printed circuit structure;

[0019] The wave transmission line may comprise a continuous metal track in the transmission direction, framing, with the electrically conductive plate, said freed volume;

[0020] The line may comprise in the general plane of symmetry a central row of metallized vias, said row framing, with the electrically conductive plate, said freed volume;

[0021] The line may comprise on either side of the general plane of symmetry rows of vias, two on the right and two on the left, together forming the electromagnetic band gap structure; the electrically conductive plate may comprise a plastic plate coated with silver; this is likely to greatly reduce the conductive losses induced by the cover, the latter then being very conductive; the electrically conductive plate may comprise a printed circuit structure covered with copper, in particular with a gold-nickel finish; the printed circuit structure may consist of a single-layer printed circuit; the electrically conductive plate may be a smooth sole or a cover; it may possibly be machined to increase the released volume;

[0022] The released volume can be filled with air or foam and air, or brought or maintained under vacuum.

[0023] The invention also relates to a method for manufacturing a wave transmission line comprising a step of placing in a printed circuit structure extending in a transmission direction of the transmission line, the printed circuit structure comprising on one face an electrically conductive metal layer forming a ground plane, metallized lateral vias drilled in the printed circuit structure, electrically connected to said metal layer and arranged on either side of a general plane of symmetry of the transmission line including the transmission direction, the vias contributing to a band gap structure of the wave transmission line a step of preparing an essentially planar face of an electrically conductive plate and an essentially planar face of the printed circuit structure opposite the metal layer forming a ground plane and a step of preparing a bonding structure,sized to secure said electrically conductive plate and the printed circuit structure by their essentially flat faces, while spacing them and electrically insulating them from each other, a step of securing the electrically conductive plate and the printed circuit structure using the adhesive structure.,

[0024] The method is particular because the adhesive structure is a sheet of double-sided adhesive and during its preparation, it is ideally perforated by cutting or thinned by making a flat, then is positioned during the joining step leaving a free volume extending in the transmission direction between the printed circuit structure and said electrically conductive plate for the propagation of waves in air, a gas or a vacuum.

[0025] This allows an air cavity to be structured using known production processes. The resulting waveguide is ultra-compact, with good performance: linear losses are very limited. In addition, there is a structure without electrical continuity between the opposite faces of the stack, which is more practical to use, but which can nevertheless contain the wave thanks to the groove-gap structure (electromagnetic bandgap structure) formed by the lateral vias.

[0026] The presentation of the invention will be continued in relation to the appended figures which are presented for illustrative purposes.

[0027] Figure 1 is an overall diagram of the transmission line according to one embodiment of the invention, seen from three-quarters, and exploded. Figure 2 is a view of the transmission line of Figure 1, in section - an enlargement of the cavity area being further presented next to the main figure.

[0028] Figure 3 is a sectional view of another embodiment of the invention, with a further enlargement of the cavity area shown adjacent to the main figure.

[0029] Figure 4 is a sectional view of another embodiment of the invention.

[0030] Figure 5 shows the steps of the method according to the invention.

[0031] [Fig. 1] Figure 1 shows the following elements constituting a wave transmission line according to a first embodiment of the invention.

[0032] A printed circuit board, also called PCB for printed circuit board in English, in this case a single-layer printed circuit 10, composed in most of its thickness of a plate of dielectric material 12, or electrical insulator, and carrying on a lower face a conductive metal layer 15, continuous and forming an electrical ground plane is used. On the other face of the layer of dielectric material, or upper face, a conductive metal layer may have been present (the initial product was therefore a stackup core), but it has been largely removed by an etching process, which leaves the dielectric material flush over a large part of the upper surface 17, the latter being essentially flat. Alternatively, no metal layer was initially present on the upper surface (the initial product was therefore a laminate). The thickness of the single-layer printed circuit 10 may be of the order of 4 mm.

[0033] The plate of dielectric material 12 is pierced right through transversely to the conductive metal layer 15 and to the upper surface 17, by vias, aligned in five rows. The vias have been formed using a drilling process, then metallized, such that they are in electrical contact with the ground plane formed by the conductive metal layer 15 forming the ground plane. They are therefore all at the same electrical potential. The central row of vias is, in the embodiment presented, made up of vias with a diameter slightly larger than that of the vias of the other rows, referred to as lateral vias 20. The five rows are arranged with respect to each other in a regular manner, and above all respecting a plane of symmetry around the central row, the vias of which are referred to as central vias 25. Within a row, the vias are spaced regularly.The mouths of the vias on the upper surface 17 can be metallized and have a metal pellet shape, which, in the case of the lateral vias 20 is a solid disc obstructing the via and constituted above the level of the plate of dielectric material 12, but with a very thin thickness, of the order of 17 to 35 μm. The mouths of the vias on the conductive metal layer 15 can be open or obstructed, and ensure the electrical connection between the via and the ground plane.

[0034] A conductive metal track 30 has been placed on the mouths of the central vias 25 on the side of the upper surface 17. It may result from the preservation along its location of the metal layer which was originally present on the upper face 17 and which was etched over the greater part of the surface, or it may also result from a metal deposition subsequent to the removal of the metal layer by etching. Preferably, the mouths of the central vias 25 are plugged by the metal layer of the track, and preferably, the metal track 30 is in electrical contact with the vias of the central row and therefore the ground plane. The metal track 30 being very thin - it is a simple deposit, with a thickness again of 17 to 35 μm - its presence does not call into question the essentially flat character of the surface 17.

[0035] The metal track 30 is symmetrically surrounded by two rows of vias on each of its sides.

[0036] On the upper surface 17 is placed a double-sided adhesive which allows the single-layer printed circuit 10 to be fixed to a cover 50, on either side of the track. The double-sided adhesive is a sheet of dielectric material coated on both sides with a tacky resin, which adheres to the surface against which the sheet is placed. It has a relatively low thickness compared to the thickness of the plate of dielectric material, but which is a little higher than the thickness of the metal track 30. This double-sided adhesive can be applied in the form of a continuous sheet and then removed from the surface of the track, by cutting, for example laser cutting, and peeling off, or it can be cut beforehand, again by laser cutting, into two pieces, each of the two pieces being applied to one side of the metal track 30. Instead of laser cutting, the perforating of the sheet of adhesive can be carried out using a die cutter.In both cases, a piece 40 or 41 of adhesive runs along one edge of the track on either of its sides and covers the plate of dielectric material 12 and the mouths of the two rows of vias. The pieces of adhesive 40 and 41 can run along the edges of the track, stopping very precisely against these edges, or run along them at a distance, leaving a space between the edge of the piece of adhesive and the edge of the metal track, or conversely, slightly cover the track, while leaving a large part of it uncovered by the adhesive.

[0037] The thickness of parts 40 and 41 can be less than 100 pm, and it is greater than 50 pm, or at least 40 pm. It can also be greater, but there is an advantage in using a thin thickness to miniaturize the structure. It is in any case much greater than the thickness of the metal pads blocking the lateral vias, and of the conductive metal track 30.

[0038] The cap 50 is a mechanical part that has a structural function and is made of silver-coated plastic material, or silver-coated aluminum alloy, or copper coated with a gold-nickel alloy finish. It has sufficient lateral dimensions to cover the five rows of vias, and at the very least, it covers the metal track 30 and is fixed to the parts 40 and 41, which immobilizes it due to the glue.

[0039] Face 52 of the cover is used to glue it to parts 40 and 41. This face is essentially flat.

[0040] Between the two parts 40 and 41, above the metal track 30 and below the cover 50, there is an elongated cavity, or tunnel 45, parallel to the metal track 30, filled by default with air, but which can also be evacuated in certain embodiments. It has the width of the metal track 30, or a little less if the adhesive has covered a marginal part of the metal track, or a little more if the adhesive does not stick to the edge of the metal track 30. It has the height of the thickness of the adhesive layer in which the parts 40 and 41 are formed.

[0041] [Fig. 2] In Figure 2, we see the structure presented in Figure 1, in section along a plane transverse to the stack formed by the plate of dielectric material 12 of the adhesive and the cover 50, and also transverse to the rows of vias and to the metal track 30. The tunnel 45 is visible, and it is specified here that instead of extending, at least on its central line, between the metal track 30 and the cover 50, it may not reach the cover, in the hypothesis where the two pieces of adhesive 40 and 41 have not been completely separated, but that there remains a thinned thickness of adhesive between them. In this hypothesis, the layer of adhesive has been previously hollowed out before applying it to the upper face 17 so as to form the tunnel 45 while retaining a ceiling formed from the material of the thinned adhesive layer, in the form of a flat.The retained part of the adhesive layer, which forms a bridge between the two parts 40 and 41 in this variant then sticks to the cover 50, but does not stick to the metal track 30.

[0042] The tunnel 45 constitutes a rectangular waveguide, between the conductive cover 50 and the metal track 30. It benefits from the presence of the two rows of vias on the left and the two rows of vias on the right to ensure a confinement effect for the transmitted wave. Generally, the wave is confined in a very thin air layer and its immediate environment, referenced 100.

[0043] [Fig. 3] In Figure 3, an alternative embodiment is shown, based on the embodiment of Figure 2, in which two trenches 70 and 71 have been added in the material of the dielectric material plate 12, parallel to the metal track 30, on either side of the latter, open on the upper surface 17, and blind on the side of the conductive metal layer which they do not reach. These trenches 70 and 71 which are local concavities in an otherwise flat surface, are not blocked by the adhesive pieces 40 and 41 which are stopped so as to leave a continuity of air between their volume and that of the tunnel 45. Thus, the trenches 70 and 71 constitute a continuous air space with the tunnel 45, closed by a perimeter in all transverse directions, between the conductive cover 50 and the metal track 30. There is therefore a U-shaped waveguide, of which the two trenches constitute the arms, and the tunnel the base.It benefits from the presence of the two rows of vias on the left and the two rows of vias on the right to ensure a confinement effect on the transmitted wave. The two branches of the U can be symmetrical or non-symmetrical.

[0044] [Fig. 5] In Figure 4, another alternative embodiment is shown, based on the embodiment of Figure 2, in which a flat 80 has been added in the material of the cover 50, parallel to the metal track 30, in line with it, open on the lower face of the cover, which faces the single-layer printed circuit 10. This flat 80, a local concavity in an otherwise flat surface, constitutes a thinning of the cover, but the latter is not pierced. Thus, the flat 80 constitutes a continuous air space with the tunnel 45, closed by a perimeter in all transverse directions. There is therefore a waveguide, in this case in the form of a rectangle, or the addition of two rectangles to each other, between the conductive cover 50 and the metal track 30. It again benefits from the presence of the two rows of vias on the left and the two rows of vias on the right to ensure a confinement effect for the transmitted wave.

[0045] Electric field calculations have shown that with these configurations, the electric field is partitioned above the metal track and circulates little in the dielectric material, which makes it possible to limit linear losses.

[0046] Alternatively, it is possible to deposit or inject into the tunnel volume a foam, composed by its structure of a significant volume proportion of air. Such foam or injected foam can also be deposited in the trenches and in the flat of the alternative embodiments.

[0047] Also, as a variant, it is possible to place between the cover and the single-layer printed circuit, not a layer of double-sided adhesive, but a multi-layer assembly having adhesive properties on the upper and lower faces, and between them a spacer layer.

[0048] [Fig. 5] Figure 5 shows the steps of the invention: during step E1, the printed circuit is prepared, in particular by drilling and metallizing the vias 20 and 25, by etching the face that will be bonded if it initially carries metal, and by depositing the track that will serve as a rib, ensuring that the thickness of the metal deposit constituting the track remains thin compared to the thickness of the adhesive that will be used to secure the printed circuit to the cover. Generally speaking, it is ensured that the surface of the printed circuit that will be used to bond the cover is flat.

[0049] During step E2, the cover is prepared, for example by silver-plating a plastic plate, and ensuring that the surface of the plate that will be used to bond the printed circuit is flat. During step E3, the double-sided adhesive that will be used is prepared. It can be protected by protective films on both sides. It is of a size that allows both sides of the rib, in other words both sides of the track, to be bonded to the cover, by extending tautly flat from one side of the track to the other. For its portion that will be at the right angle to the track, without it being essential to retain exactly the same width, the adhesive is perforated by applying a laser cutter or using a die-cutter. Thus, parts 40 and 41 shown in Figure 1 are separated.They can be completely separated, or if the opening is limited to a part of their length in the direction of propagation of the wave, then the parts 40 and 41 can remain integral at one or the other, at their two ends in the direction of propagation, or even at both ends.

[0050] Alternatively, Parts 40 and 41 may be prepared separately, and at no time have been joined.

[0051] Alternatively, the adhesive is thinned by making a flat, which removes a portion of the adhesive thickness on one side or the other of the adhesive, and preferably on the side that could have been in contact with the track. Thus, the adhesive intended to come into contact with the cover can be maintained over the entire surface, but the adhesive intended to come into contact with the track or the printed circuit is removed, as well as a portion of the adhesive thickness.

[0052] Instead of a single-layer adhesive, a multi-layer can be used, with a thickness of insulation such as foam between two adhesive layers.

[0053] The single-layer or multi-layer adhesive has a spacing function: it keeps the printed circuit board away from the conductive cover, and electrically insulates them from each other, while ensuring they remain attached to each other.

[0054] During an assembly step E4, the adhesive on both sides of the adhesive structure is activated, in particular by removing the protective films, and the cover is fixed to the printed circuit, ensuring that the edges of the parts 40 and 41 are parallel to the alignment of the central vias and / or to the edges of the metal track 30.

[0055] Instead of double-sided tape, a prepreg or glue layer can be used.

Claims

CLAIMS 1. Wave transmission line (1) comprising a printed circuit structure (10) extending in a transmission direction (D) of the transmission line, the printed circuit structure (10) comprising on one face an electrically conductive metal layer (15) forming a ground plane, the printed circuit structure (10) being, to contribute to an electromagnetic bandgap structure of the wave transmission line, pierced with metallized lateral vias (20) electrically connected to said metal layer (15) and arranged on either side of a plane (P) of general symmetry of the transmission line (1) including the transmission direction (D), the transmission line (1) further comprising an electrically conductive plate (50) and a sticky structure (40, 41), spacing and electrically insulating an essentially planar face (52), subject to local concavities,of said electrically conductive plate (50) with an essentially flat face (17), subject to local concavities, of the printed circuit structure opposite the metal layer (15) forming a ground plane, characterized in that the adhesive structure (40, 41) is thinned, or even interrupted, at the plane (P) of general symmetry, leaving a free volume (45) extending in the transmission direction (D) between the printed circuit structure (10) and said electrically conductive plate (50) for the propagation of waves in air, a gas or a vacuum., 2. Wave transmission line (1) according to claim 1, characterized in that the adhesive insulating structure (40, 41) is a single layer of double-sided adhesive material, perforated around the plane (P) of general symmetry or thinned by the presence of a flat around the same plane (P), the flat being placed on the side of the printed circuit structure.

3. Wave transmission line (1) according to claim 1 or claim 2, characterized in that it comprises a continuous metal track (30) in the transmission direction (D), framing, with the electrically conductive plate (50) said freed volume (45).

4. Wave transmission line (1) according to one of claims 1 to 3, characterized in that it comprises in the plane (P) of general symmetry a central row of metallized vias (25), said row framing, with the electrically conductive plate (50), said freed volume (45).

5. Wave transmission line (1) according to one of claims 1 to 4, characterized in that it comprises on either side of the plane (P) of general symmetry rows of vias (20) two in number on the right and two on the left, together forming the electromagnetic band gap structure.

6. Wave transmission line (1) according to one of claims 1 to 5, characterized in that the electrically conductive plate (50) comprises a silver-coated plastic plate.

7. Wave transmission line (1) according to one of claims 1 to 5, characterized in that the electrically conductive plate (50) comprises a printed circuit structure covered with copper with a gold-nickel finish.

8. Wave transmission line (1) according to one of claims 1 to 7, characterized in that the printed circuit structure (10) consists of a single-layer printed circuit.

9. Wave transmission line (1) according to one of claims 1 to 8, characterized in that the electrically conductive plate (50) is a smooth sole or a cover.

10. Wave transmission line (1) according to one of claims 1 to 9, characterized in that the released volume (45) is filled with air or foam and air, or brought or maintained under vacuum.

11. A method of manufacturing a wave transmission line (1) comprising a step of placing (El) in a printed circuit structure (10) extending in a transmission direction (D) of the transmission line, the printed circuit structure (10) comprising on one face an electrically conductive metal layer (15) forming a ground plane, metallized lateral vias (20) drilled in the printed circuit structure, electrically connected to said metal layer (15) and arranged on either side of a plane (P) of general symmetry of the transmission line (1) including the transmission direction (D), the lateral vias being for contributing to an electromagnetic bandgap structure of the wave transmission line, a step of preparing (E2) an essentially planar face (52), subject to local concavities, an electrically conductive plate (50) and a face substantially planar (17), subject to local concavities, of the printed circuit structure opposite the metal layer (15) forming a ground plane and a step (E3) of preparing a sticky structure (40, 41), dimensioned to secure said electrically conductive plate (50) and the printed circuit structure by said substantially planar faces (17, 52), while spacing them apart and electrically insulating them from each other, a step (E4) of securing the electrically conductive plate and the printed circuit structure using the sticky structure (40, 41), the method for manufacturing a wave transmission line being characterized in that the sticky structure (40, 41) is a sheet of double-sided adhesive and during its preparation (E3), it is perforated by cutting or thinned by making a flat,then is positioned during the securing step leaving a freed volume (45) extending in the transmission direction (D) between the printed circuit structure (10) and said electrically conductive plate (50) for the propagation of waves in air, a gas or a vacuum.,

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