First slide

Intensity of

Question

‘A’ sings with frequency ‘n’ and ‘B’ sings with a frequency ‘n/4’. If the energy remains the same and the amplitude of ‘A’ is ‘a’, then amplitude of ‘B’ is

Moderate

A

4a
B

2a
C

16a
D

8a

Solution

Power $= 2 π^{2} A^{2} f^{2} ρV$
Where A = Amplitude, f = Frequency, $ρ =$ density of air and V = velocity of sound in air.
$∴ 2 π^{2} A^{2} {(\frac{n}{4})}^{2} ρV = 2 π^{2} a^{2} n^{2} ρV$
$\Rightarrow A = 4 a$

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