Q. Two waves of wavelength 1.00m and 1.01m produces 10 beats in 3s. What is the velocity of the wave?
A) $150\ ms^{- 1}$
B) $115.2\ ms^{- 1}$
C) $336.6\ ms^{- 1}$
D) $200\ ms^{- 1}$
Explanation
(c) $v_{1} = \frac{v}{\lambda_{1}} = \frac{v}{1.00}\ and\ v_{2} = \frac{v}{\lambda_{2}} = \frac{v}{1.01}$
$\therefore\mathrm{\Delta}v = v_{1} - v_{2} = v\left\lbrack \frac{1}{1.00} - \frac{0}{1.01} \right\rbrack = 10$
$or\ \ v = \frac{10 \times 1 \times 1.01}{0.01} = 1010\ for\ 3s$
$\therefore v = 336.6\ ms^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.