Question

When sound waves travel from air to water, which of the following remains constant?
(A) wavelength
(B) velocity
(C) frequency
(D) phase

Answer 1

Sound waves are vibrations that travel through a medium. Here, we are expected to know about the change in characteristics of the sound wave, which are wavelength, velocity, frequency and phase, whether they change or not. Since it is propagation of vibrations, think what happens when this vibration hits the interface of two mediums, also consider the Snell’s Law in order to comment on these quantities.

Complete step by step answer: Sound waves are vibrations that propagate through medium. If you consider a point in a region where sound waves are travelling, the pressure at that point will vary according to the equation of the sound wave.

Now, consider the propagation of plane sound waves from one medium to another, meaning that the waves are planar. When the sound waves hit the interface between the mediums, refraction occurs. The whole plane does not hit at the same time, a part of it hits the interface and as a result, the waves get bent. This phenomenon is known as refraction.

Snell’s Law is used to determine the relationship between the velocities of the plane in different mediums. It is given as $\dfrac{{\sin i}}{{{v_1}}} = \dfrac{{\sin r}}{{{v_2}}}$, where $i\& r$ are the angles of incidence and refraction respectively and ${v_1}\& {v_2}$ are the velocities in medium 1 and medium 2. (propagation is from medium 1 to medium 2).

As you can see, the velocities will change after refraction. It is obvious,
because it is not possible for the wave to travel with the same velocity in other mediums. Reason being the elasticity of the medium.

Frequency of a sound wave is the rate of vibration. Now, frequency will not change even after the refraction because the frequency of the wave is determined by the source. So, the medium will have no effect on the frequency of the sound wave. The rate at which the source produces the wave will be the same in both the mediums.

The wave equation of a wave having wavelength $\lambda$, propagating with velocity $v$ and having a frequency of $n$ is given as $v = n\lambda$. This equation must be consistent. Therefore, in order to keep the frequency constant with changing velocity, wavelength has to change. And if a wave is disturbed, or is deflected, the phase will change as the waveform is changed due to refraction.

Hence, when sound waves travel from air to water, frequency remains constant.
Option (C) is correct.

Hint: Remember the wave equation, it will help you to solve questions based on refraction and also keep in mind the Snell’s Law. You must have heard that sound travels faster in some mediums, this can be used to remember that the speed of sound changes when it suffers refraction. Note that only a part of the sound wave enters the medium.