NEET Standing Wave in String and Organ Pipe MCQs & PYQs

At an open end, the pressure must remain atmospheric, establishing a pressure node. An incident high pressure pulse reflects as a low pressure pulse ((pi) phase change) to maintain this. Thus (A) is true. At a pressure node, particles have maximum displacement, which is a displacement antinode. Thus (R) is true and explains the reflection in (A).

Our ears perceive sound based on pressure variations. At a displacement node, particles have zero displacement, but pressure variations are maximum (a pressure antinode). Therefore, maximum sound is heard at a displacement node. Both (A) and (R) are true, and (R) provides the direct physical reason for (A).

Assertion (A) is true. If a transverse wave pulse propagates along the rotating hoop in a direction opposite to the hoop's rotation, and its speed relative to the string is equal to the string's linear speed, the wave appears stationary to a ground observer. Reason (R) provides this exact condition: if \(v_{\text{wave relative to string}} = -v_{\text{string}}\), then the net velocity relative to the lab frame is zero. Both are true and (R) correctly explains (A).

Assertion (A) is true by definition. Wavelength (\(lambda\)) in a longitudinal wave is the distance between two consecutive compressions or rarefactions. Reason (R) is false; a standing wave is a form of wave resulting from the superposition of two progressive waves. While it does not transfer net energy, it still represents a wave phenomenon with energy oscillation within its segments.

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.

An acoustic guitar uses the resonance of its hollow body to amplify and shape the sound produced by vibrating strings, so (A) is true. An electric guitar, being a solid-body instrument, generates sound via electromagnetic pickups sensing string vibrations, which are then amplified electronically. It does not rely on acoustic body resonance for sound production. Thus, Reason (R) is false.

In a stationary wave, displacement nodes correspond to points of maximum pressure variation (pressure antinodes) and displacement antinodes correspond to points of minimum pressure variation (pressure nodes). So, (A) is true.

At the closed end of an organ pipe, there must be a displacement node, which is a pressure antinode, meaning there is maximum pressure variation, not constant pressure. Thus, (R) is false.

Both arms of a tuning fork vibrate as a single system, thus at the same frequency. Assertion (A) is true.

For efficient sound production, the arms vibrate 180 degrees out of phase (in opposite directions), not in phase. Therefore, Reason (R) is false.

Assertion (A) is false; a stationary wave stores energy, which oscillates between kinetic and potential forms.

Reason (R) is false; energy is not converted to heat but redistributed to form the stationary wave pattern.

Assertion (A) is true. For a stretched string fixed at both ends, the \(n^{\text{th}}\) normal mode indeed has \(n\) antinodes and \(n+1\) nodes.

Reason (R) is true and correctly explains this: the fixed ends are always nodes, leading to one more node than antinode.