Two identical sound waves each of loudness - interfere constructively at a point to produce a sound level of

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The Effect of Path Difference

Two identical...

Question

Two identical sound waves each of loudness $β$ interfere constructively at a point to produce a sound level of

6 β

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3 β

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β + 3

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β + 6

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Solution

The correct option is D $β + 6$
Let the intensity of sound wave from source be I'
Then the intensity of sound wave formed due to constructive interference =4I'

We know that L=10log $_{10} \frac{I}{I_{0}}$ where $I_{0}$ is constant.
Thus, $β = l o g_{10} (\frac{I^{'}}{I_{0}})^{10}$
So, Required L= $l o g_{10} (\frac{4 I^{'}}{I_{0}})^{10}$ = $β + 6$

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Two identical sound waves each of loudness β interfere constructively at a point to produce a sound level of

The correct option is D β+6Let the intensity of sound wave from source be I'Then the intensity of sound wave formed due to constructive interference =4I'We know that L=10log10II0 where I0 is constant.Thus, β=log10(I′I0)10 So, Required L=log10(4I′I0)10=β+6

Two identical sound waves each of loudness $β$ interfere constructively at a point to produce a sound level of