Physics - Wave on String Question with Solution | TestHub

The difference between two consecutive resonant frequencies of a string fixed at both ends gives the fundamental frequency $f_1$.

$f_1=f_{n+1}-f_n=450-375=75\text{ Hz}$

The velocity of the transverse wave on the string is given by $v=\sqrt{\frac{T}{\mu }}$, where $T$ is the tension and $\mu$ is the mass per unit length.

$v=\sqrt{\frac{180}{2\times 10^{-3}}}=\sqrt{90000}=300\text{ m/s}$

The fundamental frequency is related to the length of the string $L$ by $f_1=\frac{v}{2L}$.

$75=\frac{300}{2L}\Rightarrow L=\frac{300}{150}=2\text{ m}$

The total mass of the string $M$ is the product of its mass per unit length and its length.

$M=\mu L=(2\times 10^{-3}\text{ kg/m})\times 2\text{ m}=4\times 10^{-3}\text{ kg}$

$M=4\text{ g}$

Answer: 4 gram