Physics - Wave on String Question with Solution | TestHub

For a stretched string fixed at both ends, the resonant frequencies are integral multiples of the fundamental frequency $f_0$.

The given resonant frequencies are $90\mathrm{Hz}$, $150\mathrm{Hz}$, and $210\mathrm{Hz}$. The fundamental frequency $f_0$ must be the highest common factor (HCF) of these frequencies.

$\text{HCF}(90,150,210)=30\mathrm{Hz}$

Thus, the fundamental frequency is $f_0=30\mathrm{Hz}$.

The formula for the fundamental frequency of a stretched string is:

$f_0=\frac{v}{2L}$

where $v$ is the speed of the transverse wave and $L$ is the length of the string.

Given $L=80\mathrm{cm}=0.8\mathrm{m}$, we can substitute the values into the formula:

$30=\frac{v}{2\times 0.8}$

$30=\frac{v}{1.6}$

$v=30\times 1.6=48m/s$

Answer: $48\mathrm{m}/\mathrm{s}$