Question

A tuning fork is placed near a vibrating stretched wire. A boy standing near the two hears a beat frequency $f$. It is known that frequency of tuning fork is greater than frequency of stretched wire. Match the following two columns.

Answer 1

Let the frequencies of tuning fork and stretched wire be $\nu$ and ${\nu }^{\prime }$ respectively.

Also ${\nu }^{\prime }\propto \sqrt{T}$ where $T$ is the tension in the wire

Beat frequency $b=|\nu -{\nu }^{\prime }|$ ..........(1)

Now it is given that beat frequency is $f$

Thus $f=\nu -{\nu }^{\prime }$ .........(2)

Case A: Loading wax on tuning fork will decrease $\nu$

Let $n$ be the new frequency of fork after applying wax on it.

Thus it may possible that ${\nu }^{\prime }<n<\nu$ which in result decrease $f$ and for $n<(\nu ,{\nu }^{\prime })$ implies beat frequency may increase (using 1) depending on their values.

Hence beat frequency may decrease and increase.

Case B: Filing the prongs of the fork will increase its frequency.

Thus from (2) beat frequency must increase.

Case C : Increasing the tension in the wire will increase the frequency of the string waves. Thus it may possible that ${\nu }^{\prime }<n<\nu$ which in result increase $f$ and $n>({\nu }^{\prime },\nu )$ implies beat frequency may decrease (using 1) depending on their values.

Hence beat frequency may decrease and increase.

Case D: Decreasing the tension in the wire will decrease the frequency of the string waves. Thus from (2) beat frequency must increase.