Question

In a longitudinal wave, pressure variation and displacement variation are (A) In phase (B) \(90^{\circ}\) out of phase (C) \(45^{\circ}\) out of phase (D) \(180^{\circ}\) out of phase

Short answer

In a longitudinal wave, pressure variation and displacement variation are in phase since both reach their maximum and minimum values at the same points in the waveform. Thus, their phase difference is 0 degrees. The correct answer is (A) In phase.

Step-by-step solution

Understanding Longitudinal Waves

In a longitudinal wave, the particles of the medium oscillate back and forth along the direction of the wave. Therefore, the pressure and displacement variation in the medium occur due to the oscillation of the particles in the same direction as the wave is propagating.

Pressure Variation and Displacement Variation

When the displacement of the particles in the medium is at its maximum (either toward the source or away from the source), the particles are compressed together or stretched apart. In these areas of maximum displacement, we have the highest pressure variation (either compression or rarefaction). Similarly, when the displacement of the particles is at its minimum (or zero), the pressure variation is also at its minimum (or zero).

Determining Phase Difference

Because the pressure variation and displacement variation both reach their maximum values and minimum values at the same points in the waveform, they are considered to be in phase. Therefore, the phase difference between the pressure variation and the displacement variation is 0 degrees. Hence, the correct answer to this exercise is: (A) In phase