Solution: Acoustic Pressure Wave
1. Periodicity Analysis
The wave is harmonic with a period \( T = 8 \, \text{s} \). This means the wave state repeats exactly every 8 seconds. Any snapshot taken at time \( t \) will look identical to snapshots at \( t \pm 8, t \pm 16 \), etc.
Given reference time: \( t = 10 \, \text{s} \).
Equivalent times with same phase: \( 10 – 8 = 2 \, \text{s} \), \( 10 + 8 = 18 \, \text{s} \), etc.
2. Matching Intervals
Figure-II shows two states at \( t_1 \) and \( t_2 \). The curves represent the wave at different phases. Since the wave function is sinusoidal, multiple pairs of \( (t_1, t_2) \) can produce the observed graphs depending on which cycle we are looking at.
For example:
- If the solid curve corresponds to \( t = 10 \), then a time difference of 6s or 2s could produce the dashed curve (phase shift).
- Checking the options: Pairs like (0s, 3s) or (8s, 11s) are just shifted by one full period \( T=8 \).
- Since \( t_1 \) and \( t_2 \) are just labels for “instances”, any pair separated by the correct phase difference (modulo 8s) is valid.
All given options (a, b, c, d) represent valid time intervals consistent with the wave’s period and phase structure shown in the figures.