Question

A sonometer wire vibrating in first overtone has length of 31.25 cm. Tension in the wire is 256 N and mass per unit length is $\frac{10gm}{m}$. When it is sounded together with a tuning fork, 10 beats are heard. If tension in the wire is slightly changed, no beats are heard. What is the possible frequency of the tuning fork?

• A. 502 Hz
• B. 510 Hz
• C. 505 Hz
• D. None of these

Answer 1

The correct option is A 502 Hz

Frequency of sonometer wire
$f=\frac{2}{2\times 31.25\times {10}^{-2}}\sqrt{\frac{256}{{10}^{-2}}}$
$=\frac{2\times 16\times 1000}{2\times 31.25}=512$ Hz.
So, possible frequency of tuning fork is 502 and 522 Hz.
When frequency of wire is increased by increasing tension, beats are not heard.
This may be due to
$\to$ Both frequency become equal.
(f = 522 Hz). This is also possible when frequency is decreased.
So, both the answers are possible. Only one is given in option.

Why this question? Competitives: Questions on this model are common in state level engineering entrance exams, NEET and sometimes asked in JEE mains.