First slide

Standing waves

Question

A metal wire of linear mass density of 9.8 g/m is stretched with a tension of 10 kg weight between two rigid supports 1 metre apart. The wire passes at its middle point between the poles of a permanent magnet, and it vibrates in resonance when carrying an alternating current of frequency n. The frequency n of the alternating source is

Moderate

A

25 Hz
B

50 Hz
C

100 Hz
D

200 Hz

Solution

In condition of resonance, frequency of a.c. will be equal to natural frequency of wire
$n = \frac{1}{2 l} \sqrt{\frac{T}{m}} = \frac{1}{2 \times 1} \sqrt{\frac{10 \times 9.8}{9.8 \times 10^{- 3}}} = \frac{100}{2} = 50 Hz$

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