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

Step-by-step solution

The frequency of a vibrating stretched wire is given by f = 1 2L T , where L is the wire length, T is the tension, and is the linear mass density. For resonance with the same tuning fork, f remains constant, and is unchanged. The tension T equals the weight of the hanging mass, so T = mg . At the poles, g is unchanged, but at the equator, the effective gravity is reduced to g - R ^2 , where R is Earth's radius and is its angular velocity. Consequently, T_ equator = m(g - R ^2) Since f 1 L T and f is constant, L T .