A tuning fork of frequency n produces x beats per second when sounded with a vibrating sonometer string. What must have been the frequency of the string, when a slight increase in tension produces les

Question

A tuning fork of frequency n produces x beats per second when sounded with a vibrating sonometer string. What must have been the frequency of the string, when a slight increase in tension produces lesser beats per second than before?

TestHub · Accepted Answer

Let the frequency of the tuning fork be $n$ and the frequency of the sonometer string be $f$ .

The number of beats per second is given by $x = ∣ f - n ∣$ .

This implies $f = n + x$ or $f = n - x$ .

The frequency of a sonometer string is directly proportional to the square root of its tension ( $f \propto T$ ).

When the tension in the string is slightly increased, its frequency $f$ increases.

If $f = n + x$ , an increase in $f$ will increase the difference $∣ f - n ∣$ , resulting in more beats per second.

If $f = n - x$ , a slight increase in $f$ will decrease the difference $∣ f - n ∣$ , resulting in fewer beats per second.

Since the number of beats per second decreases, the initial frequency of the string must have been $n - x$ .

Physics - Sound Wave Question with Solution | TestHub

Options:

Doubts & Discussion