A transverse progressive wave travels along a string.
The graph shows the variation with distance of the displacement of the string at time \(t=0\).
Which graph represents the variation with time of the velocity of point \(P\) on the string?
Correct Answer: \( \boxed{\mathrm{D}} \)
For a wave travelling to the right, the particle velocity is opposite in sign to the slope of the displacement-distance graph.
At point \(P\), the displacement is zero with a positive slope, so the particle initially has a negative velocity.
The particle velocity varies sinusoidally with time.
Therefore, the correct answer is (D).
Which row describes a progressive longitudinal wave?
| transfers energy in a direction parallel to the oscillations | requires a medium to travel through | always travels at the same speed | |
|---|---|---|---|
| (A) | false | false | true |
| (B) | false | true | true |
| (C) | true | false | false |
| (D) | true | true | false |
Correct Answer: \( \boxed{\mathrm{D}} \)
A progressive longitudinal wave transfers energy in the same direction as the oscillations.
Mechanical longitudinal waves require a material medium to travel through.
The speed of a wave depends on the properties of the medium, so it is not always the same.
Therefore, the correct answer is (D).
What is the phase difference between points P and Q on the progressive wave shown in the diagram?
Correct Answer: \( \boxed{\mathrm{B}} \)
Point P is at a crest. Point Q is at the next downward equilibrium crossing after one complete cycle.
The phase difference is one full cycle plus one-quarter cycle:
\(360^\circ+90^\circ=450^\circ\).
Therefore, the correct answer is (B).
