Physics - Sound Wave Question with Solution | TestHub

The frequency of a vibrating stretched string is given by $n=\frac{1}{2L}\sqrt{\frac{T}{m}}$, where $L$ is the vibrating length, $T$ is the tension, and $m$ is the linear mass density.

The tension $T$ is provided by the weight of a suspended mass $M$, so $T=Mg$, where $g$ is the acceleration due to gravity. Substituting this, we get:

$n=\frac{1}{2L}\sqrt{\frac{Mg}{m}}$

For the wire to vibrate in unison with the same tuning fork, its frequency $n$ must remain constant. For a given mass $M$ and wire $m$, this implies:

$L\propto \sqrt{g}$

The acceleration due to gravity is maximum at the poles and minimum at the equator ($g_{equator}<g_{poles}$).

Since $g$ decreases when moving from the poles to the equator, the vibrating length $L$ must also be decreased to maintain the same frequency.

Answer: should be decreased.