Question

If two waves of length $50cm$ and $51cm$ produced $12$ beats $persecond$, the velocity of sound is:

• A. $360$
• B. $340$
• C. $306$
• D. none of the above

Answer 1

The correct option is C $306$

Given,

Wavelength,

${\lambda }_1=50cm=0.5m{\lambda }_2=51cm=0.51m$

Frequency of the beats, f=12

Now, $f=\frac{V}{{\lambda }_1}-\frac{V}{{\lambda }_2}=V[\frac{1}{{\lambda }_1}-\frac{1}{{\lambda }_2}]12=V[\frac{1}{0.5}-\frac{1}{0.51}]12=V\left[\frac{0.01}{0.5\times 0.51}\right][V=306m/s]$

Hence option (C) is correct