Question

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

• A. 0.2 cm
• B. 0.4 cm
• C. 0.3 cm
• D. 0.1 cm

Answer 1

The correct option is B 0.4 cm

$f=\frac{1}{2l}\sqrt{\frac{T}{\mu }}$
Beat frequency = $\left(f_2-f_1\right|$

Here, $f_1$ = 250 Hz and beat frequency is 4.

So, $f_2$ = 250 - 4 = 246 Hz
For beat frequency to reduce to zero, $f_2$ should be equal to 250 Hz.

So, the length will be now : $\frac{25\times 246}{250}$ = 24.6 cm
This implies that the length reduction is 0.4 cm.