Question

Two waves of the same pitch have amplitudes in the ratio 2 : 5. What will be

the ratio of their (i) loudness (ii) pitch.​

Answer 1

Let the amplitudes of waves be a1 and a2. and loudness be L1 and L2.

We have been given, a1 : a2 = 2 : 5

Now,

Ratio of Loudness can be given by the factors depending loudness.

One of such factor is that loudness is  directly proportional to the square of amplitude.

or, L ∝ A²

Then ratio of loudness:

L1 / L2  = (a1)² / (a2)² = 2² / 5²

L1 / L2 = 4 / 25

Therefore, Ratio of their loudness is 4 : 25.

Since, the pitch are same, therefore, ratio of pitch is 1 : 1

Answer 2

Let the amplitudes of waves be a1 and a2. and loudness be L1 and L2.

We have been given, a1 : a2 = 2 : 5

Now,

Ratio of Loudness can be given by the factors depending loudness.

One of such factor is that loudness is  directly proportional to the square of amplitude.

or, L ∝ A²

Then ratio of loudness:

L1 / L2  = (a1)² / (a2)² = 2² / 5²

L1 / L2 = 4 / 25

Therefore, Ratio of their loudness is 4 : 25.

Since, the pitch are same, therefore, ratio of pitch is 1 : 1