Question

Two waves of the same pitch have amplitudes in the ratio $1:3$ . What will be the ratio of their intensities?

Answer 1

Initially, we write down the given information and find a relationship between them. Then we find how the information of the same pitch can be helpful to us. We define pitch and find a relation between pitch and frequency.

Complete step by step solution:
We are given two waves, let us assume their amplitudes to be ${A_1}$ and ${A_2}$ , it is given that the ratio of their amplitudes is, $1:3$
That is, $\dfrac{{{A_1}}}{{{A_2}}} = \dfrac{1}{3}$
We know that amplitude gives us an idea about how loud the sound is and frequency determines the speed of the wave.
Proceeding to the information we have on the pitch; we define pitch as the quality of a sound governed by the rate of vibrations producing it.
Since it is given that the pitch is the same for both the waves, the frequency of the two is also the same.
Hence, if two waves have the same pitch, they have the same frequencies. This allows us to conclude the ratio of frequencies of the two waves with the same pitch as, $1:1$

Note:
Pitch and frequency are often associated together but the pitch is often defined as the frequency. Pitch is a quantity that actually can be interpreted as high or low by the listener. Even though pitch and frequency are not the same things, they are correlated. The frequency and pitch of a sound wave are directly proportional. This means that when the frequency of sound waves increases, so does the pitch of the waves or vice versa.