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A source of frequency 10 kHz when vibrated over the mouth of a closed organ pipe is in unison at 300 K. The beats produced when temperature rises by 1 K is

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30 Hz

13.33 Hz

16.67 Hz

40 Hz

answer is C.

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Detailed Solution

$f = \frac{1}{4 l} \sqrt{\frac{γ R T}{M}}$
Since $Δ T < < T$

$\Rightarrow \frac{d f}{f} = \frac{1}{2} \frac{d T}{T} \Rightarrow d f = \frac{1}{2} \times \frac{1}{300} \times 10, 000 \Rightarrow d f = 16.67$

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