First slide

Beats

Question

An organ pipe, open from both ends produces 5 beats per second when vibrated with a source of frequency 200 Hz. The second harmonic of the same pipes produces 10 beats per second with a source of frequency 420 Hz. The frequency of source is

Moderate

A

195 Hz
B

205 Hz
C

190 Hz
D

210 Hz

Solution

Initially number of beats per second = 5
$∴$ Frequency of pipe = 200 $\pm$ 5 = 195 Hz or 205 Hz ...(i)
Frequency of second harmonics of the pipe = 2n and number of beats in this case = 10
$∴$ 2n = 420 $\pm$ 10 $\Rightarrow$ 410 Hz or 430 Hz
$\Rightarrow$ n = 205 Hz or 215 Hz ... (ii)
From equation (i) and (ii) it is clear that n = 205 Hz

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