Evan's Space

2017PurePhyP2Q5 Two points on the rope wave with displacement-time graphs given

In this this question, the displacement-time graphs are given, which are different from displacement-distance graphs.

In the displacement-time graphs of A and B, they show the displacement of that particular point at different timing. E,g, at t = 0s, the A is at the rest position (0 displacement) and at time 0.2 s it is at the maximum displacement. This means A is going up from t = 0 s to 0.2 s.

Solutions:
(a) Amplitude: 1.5 cm
(b)(i) Frequency is the number of complete waves produced in 1 second.
(ii) period T = 0.8s, f = 1/T = 1/0.8 = 1.25 Hz
(c) Closest possible positions of A and B, (refer to the video), is when the
time taken for the wave to move from A to B is T/4 = 0.8/4 = 0.2 s.
speed = distance/time = 38/0.2 = 190 cm/s approx. 200 cm/s
(ii) There are various possibilities in which B can be 38 cm to the right of A. Besides T/4, it can be 1.25T or 2.25 T etc. Hence the speed can be other values.

Refer to the video for the full explanation

Transverse Waves and Longitudinal Waves

Transverse waves are waves in which the direction of the wave is perpendicular to thedirection of the vibration.
e.g Light, water, and any waves in the electromagnetic spectrum

Longitudinal waves are waves in which the direction of the wave is parallel to the direction of the vibration.
e.g Sound

Wave equation: V = fλ
From the rope videos, with only vertical displacement, speed of wave is constant.
Hence frequency is inversely proportional to wavelength. [f increases, λ decreases, and vice versa]

Transverse Waves and Longitudinal Waves

Transverse waves are waves in which the direction of the wave is perpendicular to thedirection of the vibration.
e.g Light, water, and any waves in the electromagnetic spectrum

Longitudinal waves are waves in which the direction of the wave is parallel to the direction of the vibration.
e.g Sound

Wave equation: V = fλ
From the rope videos, with only vertical displacement, speed of wave is constant.
Hence frequency is inversely proportional to wavelength. [f increases, λ decreases, and vice versa]