Two waves of the same pitch have their amplitude in the ratio $2 : 3$ . What will be the ratio of their loudness?

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Solution

Step 1: Given data:
Amplitude ratio $= 2 : 3$
Step 2: Calculating the ratio of loudness:
We know that,
Loudness is directly proportional to amplitude square.
$L o u d n e s s \propto {(A m p l i t u d e)}^{2}$
So, the ratio of loudness will be equal to ${(\frac{2}{3})}^{2} = \frac{4}{9} .$
Hence, the ratio of their loudness is $\frac{4}{9} .$

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Two waves of the same pitch have their amplitude in the ratio 2:3. What will be the ratio of their loudness?

Step 1: Given data:Amplitude ratio =2:3Step 2: Calculating the ratio of loudness:We know that,Loudness is directly proportional to amplitude square.Loudness∝(Amplitude)2So, the ratio of loudness will be equal to232=49.Hence, the ratio of their loudness is 49.

Two waves of the same pitch have their amplitude in the ratio $2 : 3$ . What will be the ratio of their loudness?