Propagation Of Sound Wave - Practice Questions & MCQ

Propagation of sound waves

Sound is a longitudinal wave that is created by a vibrating source such as a guitar string, the human vocal cords, or the diaphragm of a loudspeaker. As a sound wave is a mechanical wave, so, sound needs a medium having properties of inertia and elasticity. To understand the propagation of sound waves. let us take an example - 

Consider a tuning fork producing sound waves. When prong B moves outward towards the right it compresses the air in front of it and due to compression, the pressure in this region rises slightly. The region where pressure is increased is called a compression pulse and it travels away from the prong with the speed of sound.

Now, after producing the compression pulse, prong B reverses its motion and moves inward. This process drags away some air from the region in front of it, which causes the pressure to dip slightly below the normal pressure. This region is decreased pressure region which is called a rarefaction pulse. Following immediately behind the compression pulse, the rarefaction pulse also travels away from the prong with the speed of sound. If the prongs vibrate in SHM then the pressure variation in the layer close to the prong also varies simple harmonically and shows SHM and hence increase in pressure above normal value can be written as -  

$\delta P=\delta P_0\sin \omega t$

Here, $\delta P_0$ is the maximum increase invalue above the normal value
Now, the equation can also be written as -

$\delta P=\delta P_0\sin [\omega (t-x/v)]$

where, $v$ is the wave velocity, So, the above equation shows the variation of pressure with time.
If the change in pressure is not very small then we can write the variation of pressure in the form of -

$\mathrm{\Delta }p=\mathrm{\Delta }{p}_{max}\sin [\omega (t-x/v)]$