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Standard IX

Physics

Volume or Loudness

Two identical...

Question

Two identical sounds $S_{1}$ and $S_{2}$ reach at a point $P$ in phase. The resultant loudness at point $P$ is $n d B$ higher than the loudness of $S_{1}$ . The value of $n$ is:

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Solution

Let $a$ be the amplitude due to $S_{1}$ and $S_{2}$ individually.

Loudness due to $S_{1}$ and $S_{2} = I_{1} = K a^{2}$

Loudness due to $S_{1} + S_{2} = I = K (2 a)^{2} = 4 I_{1}$

Resultant loudness at point $P$ ,

$n = 10 l o g_{10} (\frac{4 I_{1}}{I_{1}})$

$= 10 l o g_{10} (4) = 6$

Final answer: $6$

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Volume or Loudness

Standard IX Physics

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Two identical sounds S1 and S2 reach at a point P in phase. The resultant loudness at point P is n dB higher than the loudness of S1. The value of n is:

Let a be the amplitude due to S1 and S2 individually. Loudness due to S1 and S2=I1=Ka2 Loudness due to S1+S2=I=K(2a)2=4I1 Resultant loudness at point P, n=10 log10 (4I1I1) =10 log10 (4)=6 Final answer: 6

Two identical sounds $S_{1}$ and $S_{2}$ reach at a point $P$ in phase. The resultant loudness at point $P$ is $n d B$ higher than the loudness of $S_{1}$ . The value of $n$ is: