Question

Two waves of the same pitch have amplitude in the ratio 1 : 3 what will be the ratio of their loudness and pitch

Answer 1

Given:

Two waves having the same pitch.

Amplitude of both the waves are in the ratio

= 1 : 3

To Find:

Ratio of their loudness

Ratio of their pitch

Calculating:

The relation between amplitude and frequency is given by:

Loudness α (Amplitude)^2

According to the relation we calculate:

= L1 / L2 = (a1)^2 / (a2)^2

Substituting the values give to us in this we get:

= (1)^2 / (3)^2

= 1 / 9

Therefore, the ratio of their loudness would be 1 : 9.

Now we have to calculate the ratio of the pitch:

Amplitude of sound has no relation with the frequency.

If pitch is unchanged frequency remains the same

By this we can calculate the ratio of the pitch:

= Pitch of 1 st Wave / Pitch of 2 nd Wave

Substituting the values:

= 1 / 1

= 1 : 1

Therefore, the ratio of the pitch is 1 : 1.