Harmonic vs. Stationary Waves – Rankers Physics

Standing Wave in String and Organ Pipe: Practice Problem & Solution

Assertion (A): In a harmonic wave of a given frequency all particles have the same amplitude but different phases at a given time. Reason (R): In a stationary wave, all particles have the same phase at a given instant but have different amplitudes.  
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Standing Wave in String and Organ Pipe. Understanding the underlying formula is key to arriving at the correct answer below:

In a harmonic traveling wave, all particles oscillate with the same amplitude but their phases vary with position. So, (A) is true. In a stationary wave, particles between two successive nodes vibrate in phase, but particles on either side of a node are \(180^\circ\) out of phase. Their amplitudes also vary with position. So, (R) is false.

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