First slide

Beats

Question

A tuning fork and a sonometer wire were sounded together and produce 4 beats per second. When the length of sonometer wire is 95 cm or 100 cm, the frequency of the tuning fork is

Moderate

A

156 Hz
B

152 Hz
C

148 Hz
D

160 Hz

Solution

Probable frequencies of tuning fork be $n + 4$ or $n - 4$
Frequency of sonometer wire $n \propto \frac{1}{l}$
$∴ \frac{n + 4}{n - 4} = \frac{100}{95}$ or $95 (n + 4) = 100 (n - 4)$
or $95 n + 380 = 100 n - 400$ or $5 n = 780$ or $n = 156 Hz$

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