Assertion (A): In a stationary wave, all particles of the medium vibrate with the same frequency.
Reason (R): Each particle of the medium has the same amplitude.

Question

Assertion (A): In a stationary wave, all particles of the medium vibrate with the same frequency. Reason (R): Each particle of the medium has the same amplitude.

TestHub · Accepted Answer

The equation of a stationary wave is given by $y (x, t) = 2 A sin (k x) cos (ω t)$ .

From the equation, the time-dependent part is $cos (ω t)$ for all particles, which means all particles of the medium vibrate with the same angular frequency $ω$ and hence the same frequency $f = \frac{ω}{2 π}$ . Thus, Assertion (A) is correct.

The amplitude of vibration for a particle at position $x$ is given by $∣2 A sin (k x) ∣$ . This shows that the amplitude varies with the position $x$ of the particle. It is zero at the nodes and maximum at the antinodes. Thus, Reason (R) is incorrect.

Answer: (A) is correct but (R) is incorrect.

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