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

Solution Explained:

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.

Leave a Reply

Your email address will not be published. Required fields are marked *

Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. Assertion (A): When two tuning fork of frequency \(256 \text{ Hz}\) and \(324 \text{ Hz}\) are vibrating together. Beats will not be heard. Reason (R): Superposition of sound waves is possible for all frequencies of sound.  
2. Two periodic waves of intensities $I_1$ and $I_2$ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is (2008)
3. Assertion (A): In mechanical waves energy transfer takes place because of the coupling through elastic forces between neighbouring oscillating parts of the medium. Reason (R): Propagation of wave in medium is due to only elastic properties of medium.  
4. A string is fixed at both ends and the vibrations of string is given by the equation \(y = 10sin(2x)cos(2t)\) where \(x, y\) are in cm and \(t\) is in second. Nearby node from left end at \(x = 0\), is at a distance
5. For production of beats the two sources must have: (1992)