A sonometer wire of length l vibrates in its fundamental mode when excited by a tuning fork having a frequency of 416 Hz . If the length of the wire is doubled while keeping all other parameters the same, the string will

Step-by-step solution

The initial fundamental frequency of the sonometer wire is given by: f₁ = v 2l = 416 Hz When the length of the wire is doubled ( l' = 2l ), the new fundamental frequency becomes: f₁' = v 2(2l) = 1 2 ( v 2l ) = 416 2 = 208 Hz The natural frequencies of the new wire are integer multiples of its fundamental frequency, i.e., 208 Hz , 416 Hz , 624 Hz , Since the wire is excited by the same tuning fork of frequency 416 Hz , the driving frequency matches the second harmonic of the new wire. In forced oscillations, a body