Question

A wire of length $L$ having linear density of $1\times {10}^{-3}kg/m$ is stretched between two rigid supports with a tension of $40N$. It is observed that the wire vibrating in $P$ segments resonates at a frequency of $420Hz$. The next higher frequency at which the wire resonates is $490Hz$. then value of $\frac{21L}{P}$ is

Answer 1

$420=\frac{P}{2l}\sqrt{\frac{T}{M}}$ ..(1)

$420=\frac{P+1}{2l}\sqrt{\frac{T}{M}}$....(2)

from equation 1 and 2

we get $P=6$

on putting P in equation 1 we get $L=10/7m$

Hence $\frac{21L}{P}=5$