Question

Beats are produced by the superposition of two waves of nearly equal frequencies. Of the following, the correct statement is

• A. all particles of the medium vibrate simple harmpnically with frequency equal to the difference between the frequencies of component waves
• B. the frequency of beats changes, with the location of the observer
• C. the frequency of beats changes with time
• D. amplitude of vibration of particle at any point changes simple harmonically with frequency equal to one half of the difference between the component waves

Answer 1

Answer: (D)

amplitude of vibration of particle at any point changes simple harmonically with frequency equal to one half of the difference between the component waves

Answer 2

$y_{1}=A \sin \omega_{1} t, y=A \sin \omega_{2} t$ $y_{1}+y_{2}=A\left(\sin \omega_{1} t+\sin \omega_{2} t\right)$ $=2 A \sin \left(\frac{\omega_{1}+\omega_{2}}{2}\right)+\cos \left(\frac{\omega_{1}-\omega_{2}}{2}\right) t$ in case of beats $\left|\omega_{1}-\omega_{2}\right|<