Question

If two tuning forks A and B are sounded together, they produce 4 beats per sec. A is then slightly loaded with wax and same no. of beats/sec. are produced again. If frequency of A is 256, the frequency of B would be
$\begin{aligned} & \left( A \right)250 \\\ & \left( B \right)262 \\\ & \left( C \right)252 \\\ & \left( D \right)260 \\\ \end{aligned}$

Answer 1

A tuning fork is a useful illustration of how a vibrating object can produce sound. When it is hit with a rubber hammer, then the tuning fork begins to vibrate. The rear and forth vibration of the times produce disturbances of surrounding air molecules.

Complete answer:
As per given in problem that four beats per second are heard when $A$ and $B$ are sounded together, $256Hz-\nu =\pm 4Hz$
where $V$ is the frequency of $B$.

Now, loading with wax decreases the frequency of implementation.
Waxing implement $A$ would mean the frequency of $A$ has reduced such that it again produces $4$ beats per second with $B$. Thus, it's now less than $B$ by $4Hz$ and initially it had been above $B$ by $4Hz$.
$\Rightarrow 256Hz-\nu =4Hz$
$\Rightarrow \nu =252Hz$

So, the correct answer is “Option C”.

Additional Information:
Tuning forks have traditionally been worked to tune musical instruments, though electronic tuners have largely replaced them. Forks are often driven electrically by placing electronic oscillator-driven electromagnets on the brink of the prongs.

Note:
Tuning fork pitch changes slightly with temperature, due mainly to a small decrease within the modulus of elasticity of steel with increasing temperature. A change in frequency of $48$ parts per million per ${}^\circ F\text{ }\left( 86\text{ }ppm\text{ }per\text{ }{}^\circ C \right)$ is typical for a steel implement. The frequency decreases (becomes flat) with increasing temperature. Tuning forks are manufactured to possess their correct pitch at a typical temperature. the quality temperature is now $20\text{ }{}^\circ C\text{ }\left( 68\text{ }{}^\circ F \right)$, but $15\text{ }{}^\circ C\text{ }\left( 59\text{ }{}^\circ F \right)$ is an older standard. The pitch of other instruments is additionally subject to variation with natural process.