At poles, a stretched wire of a given length vibrates in unison with a tuning fork. At the equator, for same setting, to produce resonance with same fork, the vibrating length of wire

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The frequency of vibration of a stretched string is given by $n = \frac{1}{2 L} \frac{T}{m}$ .

The tension $T$ in the wire is provided by a suspended mass $M$ , so $T = M g$ .

Substituting this into the frequency formula gives $n = \frac{1}{2 L} \frac{M g}{m}$ .

For resonance with the same tuning fork, the frequency $n$ remains constant. Since $M$ and the linear mass density $m$ are also constant, we get $L \propto g$ .

The acceleration due to gravity is less at the equator than at the poles ( $g_{e q u a t or} < g_{p o l es}$ ).

Therefore, $L_{e q u a t or} < L_{p o l es}$ .

To produce resonance at the equator, the vibrating length of the wire should be decreased.

Answer: should be decreased.

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