Question

A sound wave passes from a medium A to a medium B. The velocity of sound is greater than that in A. Assume that there is no absorption or reflection of the boundary. As the wave move across the boundary, the
A. Frequency of sound will increase.
B. Wavelength of sound will increase.
C. Wavelength of sound will decrease.
D. Intensity of sound will increase.

Answer 1

Hint: Use the relation between frequency, wavelength and velocity of the wave. The frequency remains constant for any wave. Recall the dependence of absorption of the sound at the boundary with the intensity of the wave.

Complete step by step answer:
We know the relation between frequency f, wavelength and velocity v of the wave.
\[v = f\lambda \]
\[ \Rightarrow \lambda = \dfrac{v}{f}\]
Therefore, from the above equation, the wavelength of sound waves is directly proportional to the velocity.
We need to verify every given option.
Frequency of sound does not depend upon the wavelength and velocity. Therefore, even if the velocity increases in the medium B, the frequency of the sound wave will remain the same.
We know that the wavelength of sound waves is proportional to the velocity. Therefore, the wavelength of the sound wave will also increase in the medium B.
The wavelength of sound will increase in the medium B.
The intensity of sound decreases as there is absorption at the boundary between the two mediums. The absorption at the boundary is proportional to the frequency of the sound wave. Since the frequency of the sound is constant, there is no absorption at the boundary. Therefore, the intensity of sound will not change.

So, the correct answer is “Option B”.

Note:
The frequency of sound wave and light wave both does not change with the change in velocity of wavelength of the wave. The absorption of the sound at the boundary is a vast phenomenon and we should only consider the dependence of absorption with intensity of the sound for this question.