Physics - Sound Wave Question with Solution | TestHub

Given frequency $f=415\text{ Hz}$ and velocity $v=332\text{ m/s}$.

The wavelength of the sound wave is:

$\lambda =\frac{v}{f}=\frac{332}{415}\text{ m}$

$\lambda =0.8\text{ m}=80\text{ cm}$

For a pipe closed at one end, the resonating lengths are given by odd multiples of $\frac{\lambda }{4}$:

$L=(2n-1)\frac{\lambda }{4}$ where $n=1,2,3,\dots$

The possible resonating lengths are:

$L_1=1\times \frac{80}{4}=20\text{ cm}$

$L_2=3\times \frac{80}{4}=60\text{ cm}$

$L_3=5\times \frac{80}{4}=100\text{ cm}$

Among the given options, $40\text{ cm}$ is an even multiple of $\frac{\lambda }{4}$ and therefore is not a resonating length.