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

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

Tardigrade Admin · Accepted Answer

As y=Ab sin (2 π na v t) where Ab=2 A cos (2 π nA t) where nA=(n1-n2/2) 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.

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

The particles vibrate simple harmonically, with the frequency equal to the difference in the component frequencies

The amplitude of vibration at any point changes simple harmonically with a frequency equal to the difference in the frequencies of the two waves

The frequency of beats depends upon the position, where the observer is

The frequency of beats changes as the time progresses

As $y = A_{b} sin (2 π n_{a v} t)$
where $A_{b} = 2 A cos (2 π n_{A} t)$
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.

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

The particles vibrate simple harmonically, with the frequency equal to the difference in the component frequencies

The amplitude of vibration at any point changes simple harmonically with a frequency equal to the difference in the frequencies of the two waves

The frequency of beats depends upon the position, where the observer is

The frequency of beats changes as the time progresses

As y=Ab​sin(2πnav​t) where Ab​=2Acos(2πnA​t) where nA​=2n1​−n2​​ 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.

As $y = A_{b} sin (2 π n_{a v} t)$
where $A_{b} = 2 A cos (2 π n_{A} t)$
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.