Question

A sonometer wire under 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 mass 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 sec. Then the speed with which the tuning fork is moved, if the speed of sound in air is 330 m/s

• A. 0.82 m/s
• B. 1.5 m/s
• C. 3 m/s
• D. 6 m/s

Answer 1

The correct option is A 0.82 m/s

Frequency, $f=\frac{1}{2l}\sqrt{\frac{1}{\mu }}$ $=\frac{1}{2\times 10\times {10}^{-2}}\sqrt{\frac{64}{{10}^{-2}}}$ $=\frac{8}{2\times {10}^{-2}}=400$

As it produces one beat per sec, $f=399Hz$

$n_1=\left(\frac{v}{v+v_s}\right)n$

$399=\left(\frac{330}{330+v_s}\right)400$

$\Rightarrow v_s=0.82m{s}^{-1}$