First slide

Travelling wave

Question

If the amplitude of sound is doubled and the frequency reduced to one-fourth, the intensity of sound at the same point will be

Moderate

A

Increased by a factor of 2
B

Decreased by a factor of 2
C

Decreased by a factor of 4
D

Unchanged

Solution

$I = 2 π^{2} a^{2} n^{2} vρ \Rightarrow I \propto a^{2} n^{2} \Rightarrow \frac{I_{1}}{I_{2}} = {(\frac{a_{1}}{a_{2}})}^{2} \times {(\frac{n_{1}}{n_{2}})}^{2}$
$= {(\frac{1}{2})}^{2} \times {(\frac{1}{1 / 4})}^{2} \Rightarrow I_{2} = \frac{I_{1}}{4}$

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