Question

When a stretched string of length L is vibrating in a particular mode, the distance between two nodes on the string is l. The sound produced in this mode of vibration constitutes the n^th overtone of the fundamental frequency of the string –

• A. L = (n + 1)l
• B. L = (n – 1) l
• C. L = nl
• D. L = (n + 1/2) l

Answer 1

Answer: (A)

L = (n + 1)l

Answer 2

l = $\frac{\lambda}{2}$ Ž l = 2l

\ n = $\frac{v}{\lambda}$ = $\frac{v}{2\mathcal{l}}$= (n + 1) $\frac{v}{2\mathcal{l}}$

\ L = (n + 1) l