First slide

Stationary waves

Question

A tuning fork vibrating with a sonometer having 20 cm wire produces 5 beats per second. The beat frequency does not change if the length of the wire is changed to 21 cm. the frequency of the tuning fork (in Hertz) must be

Moderate

A

200
B

210
C

205
D

215

Solution

Let the frequency of tunning fork be N
As the frequency of vibration string $\propto \frac{1}{length of string}$
For sonometer wire of length 20 cm, frequency must be (N + 5) and that for the sonometer wire of length 21cm, the frequency must be (N – 5) as in each case the tunning fork produces 5 beats/sec with sonometer wire
Hence $n_{1} l_{1} = n_{2} l_{2} \Rightarrow (N + 5) \times 20 = (N - 5) \times 21$
$\Rightarrow N = 205 Hz .$

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