Question

In this experiment, we have claimed to measure the speed of sound in air. To do this, we have used an audible frequency sweep. Why can we claim that the speed of sound will be the same over the bandwidth of the sweep? Is this assertion justified based on your results from experiment 2? Hint: Consider how sound (longitudinal pressure waves) propagate in a medium. (5 pts)

Answer 1

The speed of sound depends on the medium.

The sound waves are longitudinal waves i.e., the vibration of molecules will be parallel to the propagation of wave. So the energy transfer will be in a direction parallel to the movement of atoms and molecules. Further, the wve propagates by compressions and rarefactions i.e., successive compression of air medium and by expansion of air medium.

Now the experiment is to find out the speed of sound. The speed of sound mainly depends on two physical properties. They are density of the medium and temperature. They are related by the following expression.

Where, gamma is the adiabatic constnat, R is gas constant, M is molecular mass of gas and T is the absolute temperature. We can see that the first three parameters are characteristic of the gas (not R).

so speed of sound will be constant irrespective of the frequency. When the frequency changes it is only the wavelength which changes accordingly to keep the speed constant.

according to the relation.

where vs is the speed of sound and lambda is the wavelength. so we can say that the frequency and wavelength are inversely proportional to each other keeping velocity constant.