A stretched string of length 1.00m and linear mass density 1.0×10−2kgm−1 is kept under a tension of 100N. It vibrates in its fifth harmonic.
(i) Derive an expression that relates the frequency of the nth harmonic to the tension, length, and linear density of the string.
(ii) The string is now shortened to 0.80m by fixing one end at a new point. Determine the value of tension that must be applied to the shorter string so that it continues to produce the same frequency as before while vibrating in its fifth harmonic.
(iii) Calculate the percentage change in tension required.