Physics - Sound Wave Question with Solution | TestHub

Wavelength of sound is given by $\lambda =\frac{v}{f}=\frac{340}{340}=1\text{ m}=100\text{ cm}$.

For a tube closed at one end (by water), the length of the air column for resonance is given by $L=(2n-1)\frac{\lambda }{4}$, where $n=1,2,3,\dots$

Substituting $\lambda =100\text{ cm}$, the possible lengths of the air column are:
$L=25\text{ cm},75\text{ cm},125\text{ cm},\dots$

Since the total height of the tube is $120\text{ cm}$, the valid lengths of the air column are $25\text{ cm}$ and $75\text{ cm}$.

The height of the water column is $h=120-L$.

For the minimum height of water, the length of the air column must be maximum. Thus, $L_{max}=75\text{ cm}$.

Minimum height of water $=120-75=45\text{ cm}$.

Answer: 45 cm