### Waves - Result Question 38

#### 39. A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of $27^{\circ} C$ two successive resonances are produced at $20 cm$ and $73 cm$ of column length. If the frequency of the tuning fork is $320 Hz$, the velocity of sound in air at $27^{\circ} C$ is

[2018]

(a) $330 m / s$

(b) $339 m / s$

(c) $300 m / s$

(d) $350 m / s$

## Show Answer

#### Answer:

Correct Answer: 39. (b)

Solution:

- (b) Two successive resonance are produced at $20 cm$ and $73 cm$ of column length

$ \begin{matrix} \therefore \quad & \frac{\lambda}{2}=(73-20) \times 10^{-2} m \\ \Rightarrow \quad & \lambda=2 \times(73-20) \times 10^{-2} \\ & \text{ Velocity of sound, } v=n \lambda \\ & =2 \times 320[73-20] \times 10^{-2} \\ & =339.2 ms^{-1} \end{matrix} $

For closed organ pipe, third harmonic $n=\frac{(2 N-1) V}{4 \ell}=\frac{3 V}{4 \ell}(\because N=2)$

For open organ pipe, fundamental frequenty

$ \begin{aligned} & n=\frac{N V}{2 \ell}=\frac{V}{2 \ell^{\prime}}(\because N=1) \\ & \text{ According to question, } \frac{3 V}{4 \ell}=\frac{V}{2 \ell^{\prime}} \\ \Rightarrow \quad & \ell^{\prime}=\frac{4 \ell}{3 \times 2}=\frac{2 \ell}{3}=\frac{2 \times 20}{3}=13.33 cm \end{aligned} $