Two waves of the same pitch have their amplitudes in the ratio $3 : 4$ .
What will be the ratio of their loudness?

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Solution

Given:
The ratio of amplitude = $3 : 4$
To calculate: Ratio of loudness
Step 1: Relation between amplitude and loudness:
$l o u d n e s s \propto {(a m p l i t u d e)}^{2}$
Step 2: Calculation of ratio of loudness
⇒ $R a t i o o f l o u d n e s s = {(R a t i o o f a m p l i t u d e)}^{2}$
⇒ $R a t i o o f l o u d n e s s = {(\frac{3}{4})}^{2}$
⇒ $R a t i o o f l o u d n e s s = \frac{9}{16}$
Hence, the ratio of loudness will be $9 : 16$

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