Physics - Sound Wave Question with Solution | TestHub

The wavelength of the sound wave is given by:

$\lambda =\frac{v}{f}=\frac{340}{340}=1\text{ m}$

For a resonance tube closed at one end (the water surface acts as the closed end), the length of the air column for resonance is:

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

Substituting $\lambda =1\text{ m}$, the possible lengths of the air column are:

$L=0.25\text{ m},0.75\text{ m},1.25\text{ m},1.75\text{ m},\dots$

Since the total height of the tube is $1.5\text{ m}$, the maximum possible length of the air column that can be formed inside the tube is $L_{\text{max}}=1.25\text{ m}$.

The height of the water column is the total height of the tube minus the length of the air column. For the minimum height of the water column, the length of the air column must be maximum.

$h_{\text{min}}=H-L_{\text{max}}$

$h_{\text{min}}=1.5-1.25=0.25\text{ m}=25\text{ cm}$

Answer: 25 cm