Question

Which one of the following statements is not correct?
(A) The velocity of sound in air is independent of pressure.
(B) The velocity of sound in air increases with increase of temperature.
(C) The velocity of sound in air decreases as humidity increases.
(D) The velocity of sound in air is not affected by the change in amplitude and frequency.

Answer 1

Hint: Air consists of various particles like water vapor, oxygen molecules, carbon dioxide, nitrogen, etc. The changes in some parameters like pressure, temperature, humidity, frequency and amplitude may or may not affect the velocity of sound. In this question we have to refer to the probable changes of velocity of sound with respect to these parameters.

Complete step by step solution:
The velocity of sound in air is independent of pressure. This is because for the ideal gas equation, it has been seen that the pressure and density terms contribute equivalently to the speed of sound thereby cancelling each other and leading to the persistence of only the effect of temperature. So, A is a correct statement.
Sound is a form of energy and is also affected by temperature changes. As temperature changes occur, there is change in the molecular motion of the air particles simultaneously. For example, as the temperature rises the molecules have high energy and hence, they vibrate at a faster rate due to which the molecular motion fastens and hence the sound can travel faster. So, the velocity of sound in air increases with increase in temperature. Thus, B is a correct statement.
Air contains molecules of water, oxygen, nitrogen, carbon dioxide and other gases. As the humidity of air increases, the percentage of air molecules, i.e., water molecules also increase. With the increase in humidity, the density of air changes. Water molecules are lighter than other air molecules and hence the density, i.e., unit mass per unit volume decreases . As the density lowers sound can travel faster. So, with an increase in humidity the velocity of sound in air must increase. Thus, C is not a correct statement.
Calculation of speed of sound is done using the product of wavelength and frequency. But it has been seen that the change in frequency does not affect the velocity of sound.
Hence, D is a correct statement.

Note:
The velocity of sound in air is $ 333m{s^{ - 1}} $ at room temperature. But as temperature rises the velocity of sound also increases due to the increase in molecular motions. The velocity of the sound at $ {200^ \circ }C $ is noted to be around $ 436m{s^{ - 1}} $ .