Question

When beats are produced by two progressive waves of nearly the same frequency, which one of the following is correct?

• A. The particles vibrate simple harmonically, with the frequency equal to the difference in the component frequencies
• B. The amplitude of vibration at any point changes simple harmonically with a frequency equal to the difference in the frequencies of the two waves
• C. The frequency of beats depends upon the position, where the observer is
• D. The frequency of beats changes as the time progresses

Answer 1

Answer: (B)

As $y=A_{b} \sin \left(2 \pi n_{a v} t\right)$
where $A_{b}=2 A \cos \left(2 \pi n_{A} t\right)$
where $n_{A}=\frac{n_{1}-n_{2}}{2}$
Hence, the amplitude of vibration at any point changes simple harmonically with a frequency equal to the difference in the frequencies of the two waves.