Question

On producing the waves of frequency $1000Hz$ in a Kundt's tube, the total distance between $6$ successive nodes is $85cm$ . Speed of sound in the gas-filled in the tube is

• A. $300m{s}^{-1}$
• B. $350m{s}^{-1}$
• C. $340m{s}^{-1}$
• D. $330m{s}^{-1}$

Answer 1

Answer: (C)

Frequency of wave, $\nu =1000Hz$
Number of successive nodes $=6$
The total distance between six successive nodes = $85cm$
From the relation between the distance of nodes and wavelength of the wave
$\text{s}=85=\frac{\left(\text{n}-1\right)\lambda }{2}=\frac{\left(6-1\right)\lambda }{2}=\frac{5\lambda }{2}$
where, $\lambda$ = wavelength of the wave
$\therefore \lambda =\frac{2\times 85}{5}=34\text{cm}=0\text{.}34\text{m}$
Hence, the speed of sound in the gas = v $\lambda$
$=1000\times 0.34=340m{s}^{-1}$