A sonometer wire under a tension of 64 N, vibrating in its fundamental mode, is in resonance with a vibrating tuning fork. The vibrating portion of the sonometer wire has a length of 10 cm and a mass

Question

A sonometer wire under a tension of 64 N, vibrating in its fundamental mode, is in resonance with a vibrating tuning fork. The vibrating portion of the sonometer wire has a length of 10 cm and a mass of 1 g. The vibrating tuning fork is now moved away from the vibrating wire at a constant speed and an observer standing near the sonometer hears one beat per second. Calculate the speed with which the tuning fork is moved, if the speed of sound in air is 300 m/s.

Answer:

0.75

Solution:

$μ = 0.01$ kg/m, $f = \frac{1}{2 L} T / μ = 400$ Hz. Receding fork: $f^{'} = \frac{400 \times 300}{300 + u} = 399$ gives $u = 0.75$ m/s.

TestHub · Accepted Answer

μ = 0.01 kg/m, f = 2 L 1 ​ T / μ ​ = 400 Hz. Receding fork: f ′ = 300 + u 400 × 300 ​ = 399 gives u = 0.75 m/s.

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