Question

In a resonance tube experiment when the tube is filled with water up to a height of $17.0cm$ from the bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of $24.5cm$. If the velocity of sound in air is $330m/s$, the tuning fork frequency is:

• A. $2200Hz$
• B. $550Hz$
• C. $3300Hz$
• D. $1100Hz$

Answer 1

The correct option is A

$2200Hz$

Step 1: Given terms

First resonance height, $l_1$=$17\mathrm{cm}$

Second resonance height, $l_2$=$24.5\mathrm{cm}$

Velocity of sound in air = $\mathrm{v}=330{\mathrm{ms}}^{-1}$

Step 2: Formula

The velocity of sound is given as $v=2f(l_1-l_2)$

Step 3: Calculation

On substituting the given values in the formula, we get:

$\Rightarrow 330=2\mathrm{f}(24.5-17)\times {10}^{-2}$

$\Rightarrow 165=\mathrm{f}\times 7.5\times {10}^{-2}$

$\Rightarrow \mathrm{f}=\frac{165\times 100}{7.5}$

$\Rightarrow \mathrm{f}=2200Hz$

Therefore, the tuning fork frequency is $2200\mathrm{Hz}$.

Hence, option A is the correct answer.