Waves - Result Question 62
64. Two waves of lengths $50 cm$ and $51 cm$ produce 12 beats per sec. The velocity of sound is [1999]
(a) $306 m / s$
(b) $331 m / s$
(c) $340 m / s$
(d) $360 m / s$
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Answer:
Correct Answer: 64. (a)
Solution:
- (a) Given : Wavelength of first wave $(\lambda_1)$
$=50 cm=0.5 m$
Wavelength of second wave $(\lambda_2)$
$=51 cm=0.51 m$
frequency of beats per $\sec (n)=12$.
We know that the frequency of beats,
$n=12=\frac{v}{\lambda_1}-\frac{v}{\lambda_2}$
$\Rightarrow 12=v[\frac{1}{0.5}-\frac{1}{0.51}]$
$=v[2-1.9608]=v \times 0.0392$
or, $v=\frac{12}{0.0392}=306 m / s$
[where, $v=$ velocity of sound]
