A stretched wire 75cm long emits a fundamental frequency of 300Hz.By how much the length be changed so that it emits a fundamental note of 450Hz?

Answer 1

The frequency of the fundamental mode of oscillation is inversely proportional to length of string, so we can write L2/L1 = f1/f2 where L and f are length and frequency respectively, and subscripts 1 & 2 refer to 2 different cases of f & L.

Using your data we get L2 = f1*L1/f2 = 50cm Change of length = -25cm.

Alternatively you could argue that the frequency rises by a factor 3/2, so the length falls by a factor 2/3 to get the new length of 50cm...

Answer 2

Qn.1.Ans.25cm