Sound wave travels with a velocity of 300 , m , s^ -1 through a g… - Vidyadip

MCQ

Sound wave travels with a velocity of $300\, m\, s^{-1}$ through a gas. $9\, beats$ are produced in $3\, s$ when two waves pass through it simultaneously. If one of the waves has $2\, m$ wavelength, the wavelength of the other wave is ..... $m$

A
$1.98$
✓
$2.04$
C
$2.06$
D
$1.99$

✓

Answer

Correct option: B.

$2.04$

b
No. of beats per second $=\frac{9}{3}=3 \mathrm{s}^{-1}$

No. of beats per second $=v_{1}-v_{2}$

$3=\frac{\mathrm{v}}{\lambda_{1}}-\frac{\mathrm{v}}{\lambda_{2}}=\mathrm{v}\left[\frac{1}{\lambda_{1}}-\frac{1}{\lambda_{2}}\right]$

$\frac{3}{300}=\frac{1}{2}-\frac{1}{\lambda_{2}}$

$\frac{1}{\lambda_{2}}=\frac{1}{2}-\frac{1}{100}=\frac{50-1}{100}=\frac{49}{100}$

$\lambda_{2}=\frac{49}{100}=2.04 \mathrm{\,m}$

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