Physics - Wave on String Question with Solution | TestHub

The frequency of the $n^{th}$ harmonic of a stretched wire fixed at both ends is given by $f_n=n{f}_1$, where $f_1$ is the fundamental frequency.

For the $P^{th}$ harmonic, the frequency is given as:

$f_P=P{f}_1=320$

The next higher resonant frequency corresponds to the $(P+1{)}^{th}$ harmonic:

$f_{P+1}=(P+1)f_1=400$

Dividing the two equations, we get:

$\frac{P+1}{P}=\frac{400}{320}$

$\frac{P+1}{P}=\frac{5}{4}$

$5P=4P+4$

$P=4$

Answer: $4$