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I know that in solids sound can be a transverse wave and that in gases it is a longitudinal wave. The question is what happens at the boundry at the two substances? What is the mechanism of conversion of transverse into longitudinal waves?

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Imagine a metal rod and you hit one end of it with a hammer.
A compression pulse travels down the rod and back again after reflection at the other end and the cycle of reflections is repeated - this is a longitudinal wave motion.
However as the pulse travels down the rod I would imagine that the walls of rod bulge out and then return, so this is equivalent to a transverse wave.
That bulging out then compresses and rarefies the air in the vicinity of the rod and so you get longitudinal waves in air produced.

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Sound is a longitudinal wave and propagates from the solid into the gas as a longitudinal wave.

It is possible to get transverse waves in solids and they are generally known as shear waves. However we would not normally describe a shear wave as a sound wave. Shear waves in a solid will not propagate into a gas. They would simply reflect off the solid gass interface and head back into the solid.

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    $\begingroup$ There is a possibility of wave conversion when the shear waves are reflected. However, it has really low significance from the energy and power point of view. $\endgroup$ Jan 25, 2016 at 11:29
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Basically, if a transverse wave strikes a flat solid/gas boundary straight on - at an angle of incidence that is zero in relation to the normal, it will be totally reflected back into the solid. However, if it strikes at an angle, it will have particle movement both transverse and longitudinal relative to the boundary. The transverse part will be reflected back into the solid, but the longitudinal part will propagate into the gas.

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When a longitudinal waves hits a solid interface at an angle, some of the energy can cause particle movement in the transverse direction. The L-wave is mode converting to a transverse wave, following Snell's law. This mode conversion occurs because the wave encounters an interface between materials of different acoustic impedances and the incident angle is not normal to the interface. A good way to visualize this is a truck driving from asphalt to a muddy field at an angle. Let's say the front passenger tire hits the muddy field first. As the impedance changes from asphalt to mud, the truck will start to pull to the passenger side. This slight change in direction represents the refraction of the wave. In a solid medium, a portion of an L-wave wave will propagate as a transverse wave (some will continue on as a reflected longitudinal wave). Snell's Law also works to calculate how a transverse wave can mode convert back to an L-Wave at an interface, however, the energy of the resulting L-wave will be very small due to how much less energy a transverse wave carries relative to an L-wave and the effects of attenuation.

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