temperature of $27^\circ\text{C}$, two successive resonances are produced at $20\text{ cm}$ and $73\text{…
temperature of $27^\circ\text{C}$, two successive resonances are produced at $20\text{ cm}$ and $73\text{ cm}$ of column length. If the frequency of the tuning fork is $320\text{ Hz}$, the velocity of sound in air at $27^\circ\text{C}$ is [NEET 2018]
(a) $350\text{ ms}^{-1}$
(b) $339\text{ ms}^{-1}$
(c) $330\text{ ms}^{-1}$
(d) $300\text{ ms}^{-1}$
Solution
For first resonance, $l_1 = \frac{\lambda}{4}$
For second resonance, $l_2 = \frac{3\lambda}{4}$
$\therefore (l_2 - l_1) = \frac{3\lambda}{4} - \frac{\lambda}{4}$
or $\lambda = 2(l_2 - l_1)$ ...(i)
As, velocity of sound wave is given as
$v = \nu\lambda$
where, $\nu$ is the frequency.
$\Rightarrow v = \nu[2(l_2 - l_1)]$ ...(ii)
[From Eq. (i)]
Here, $\nu = 320\text{ Hz}$, $l_2 = 0.73\text{ m}$, $l_1 = 0.20\text{ m}$ (Given)
Putting the values in Eq. (ii), we get
$v = 320[2(0.73 - 0.20)] = 2 \times 320 \times 0.53$
$= 339.2\text{ ms}^{-1} \simeq 339\text{ ms}^{-1}$