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A tuning fork of frequency 250Hz produces 4 beats per second with a wire of length 25cm vibrating in its fundamental mode. The beat frequency decreases when the length is slightly shortened keeping the tension unchanged. What could be the minimum length by which the wire be shortened so that it produces no beats with the tuning fork?

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0.2 cm

0.4 cm

0.3 cm

0.1 cm

answer is B.

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Detailed Solution

Fundamental frequency $\large n\, = \frac{1}{{2l}}\sqrt {\frac{T}{\mu }}$

$\large \therefore \,nl\, = \,\frac{1}{2}\sqrt {\frac{T}{\mu }} \, = \,cons\tan t$

Fundamental frequency of 25cm long wire = (250-4) Hz

$\large {n_1}{l_1}\, = \,{n_2}{l_2}\,\, \Rightarrow \,246 \times 25\, = \,250{l_2}$

$\large {l_2}\, = \,24.6\,\, \Rightarrow \,{l_1} - {l_2}\, = \,0.4cm$

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