Question

Two waves of wavelengths 2 m and 2.02 m respectively moving with the same velocity superpose to produce 2 beats /s. The velocity of the wave is:

• A. 400 m/s
• B. 402 m/s
• C. 404 m/s
• D. 406 m/s

Answer 1

Answer: (C)

404 m/s

$\delta =\frac{v}{\lambda }$
So, ${\delta }_1=\frac{v}{{\lambda }_1}$ ${\delta }_2=\frac{v}{{\lambda }_2}$
$beat={\delta }_1-{\delta }_2$
$beat=\frac{v}{{\lambda }_1}-\frac{v}{{\lambda }_2}$
$2=v(\frac{1}{2}-\frac{1}{2.02})$
$v=\frac{2\times 2\times 2.02}{0.02}$$=404m/s$