Question

Find out the relationship between the frequency and amplitude of a sound wave:
A. Frequency is proportional to amplitude
B. Frequency is proportional to the square of the amplitude
C. Frequency is inversely proportional to amplitude
D. Frequency is inversely proportional to the square of the amplitude
E. Frequency and amplitude are independent

Answer 1

Hint: A good starting point would be to think of what amplitude of a sound wave depends on and what its frequency depends on. Do they have common dependencies? In other words, amplitude depends on the source of the sound whereas frequency depends on the number of compressions and rarefactions imparted to the medium surrounding the sound.

Complete step-by-step answer:
Let us first distinguish between amplitude and frequency.
The amplitude of a wave can be defined as the maximum displacement made by a point on a vibrating wave from its equilibrium position. It is basically the height of the wave measured in metres. For example, the amplitude of a pendulum is the distance it travels from its mean position till the half-way point of its complete path.
The frequency of a wave is the number of vibrations(cycles) executed by a body in periodic motion, measured per second. A wave with a larger frequency would fit more wave cycles into every second. For example, the frequency of a simple pendulum is the number of back and forth swings it executes or the number of times it returns to its mean position in one second.
Amplitude lends to the wave the strength of the vibrations or loudness whereas frequency determines the number of vibrations executed by the wave in one second, thereby adding to the shrill or bass of the sound wave and determines the pitch of the sound.
Time period is defined as the time taken by the wave to complete one cycle of vibration and is measured in second.
From the definition of frequency, we understand that frequency depends on the time period of the sound wave. The larger the frequency the lesser the time period. So, frequency and time period are inversely proportional to each other.
However, the amplitude of the wave and the frequency of its vibrations do not impose any influence on each other, since amplitude in a progressive sound wave is a constant and is independent of the time period whereas frequency depends on the time period.

So, the correct answer is “Option E”.

Note: Note that in some cases the loudness (amplitude) of the wave may get masked by the shrillness (high frequency) of the wave itself but this is due to interference of the two parameters after the wave is produced and there is ultimately no innate dependence arising between them either before or during wave production. This means that the magnitude of loudness of the wave is in no way dependent on the shrillness of the wave or vice versa, which is indicative of the fact that consequently, the frequency of the wave and amplitude of the wave are independent of each other.