First slide

Beats

Question

A tuning fork of frequency 480 Hz produces 10 beats per second when sounded with a vibrating sonometer string. What must have been the frequency of the string if a slight increase in tension produces lesser beats per second than before

Moderate

A

460 Hz
B

470 Hz
C

480 Hz
D

490 Hz

Solution

If suppose n_S = frequency of string $= \frac{1}{2 l} \sqrt{\frac{T}{m}}$
n_f = Frequency of tuning fork = 480 Hz
x = Beats heard per second = 10
as tension T increases, so n_S increases ( $↑$ )
Also it is given that number of beats per sec decreases (i.e. x $↓$ )
Hence n_S $↑$ – n_f = x $↓$ ... (i) $\to$ Wrong
n_f – n_S $↑$ = x $↓$ ... (ii) $\to$ Correct
$\Rightarrow$ n_S = n_f – x = 480 – 10 = 470 Hz.

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