A wire of linear mass density 9.0×10−4kgm−1 is stretched over a sonometer. The length between the two movable bridges is adjusted so that the wire, under a tension of 64N, produces exactly the same frequency as an unknown tuning fork S when both are sounded. The length required is found to be 0.80m.
Because of unavoidable experimental uncertainty, the beat method is now employed to determine the fork frequency more precisely.
(i) The bridges are first set at 0.80m. With this setting, 2 beats per second are heard. Explain what this observation tells you about the relative frequencies of the wire and the fork.
(ii) The length is now reduced to 0.78m, keeping the tension the same. The beat frequency rises to 8 beats per second. Deduce the exact frequency of the tuning fork S.
(iii) Assuming that the only significant source of uncertainty is the measurement of beat frequency (±1Hz), calculate the maximum percentage uncertainty in the value of the fork frequency obtained.