Question

A student is sending pulses of a transverse sinusoidal wave to the right along a string by whipping it up and down. With the help of a high-speed camera, plot the displacement.

Answer 1

A transverse sinusoidal wave created along a string can be modeled with a wave equation to plot the displacement of points, which follows simple harmonic motion, up and down between +A and -A, with velocity and wavelength derived from the fundamental properties of the wave.

Step-by-step explanation:

Modeling a Transverse Sinusoidal Wave

When a student sends pulses of a transverse sinusoidal wave along a string, the displacement of points on the string follows simple harmonic motion. Each point oscillates up and down between a maximum displacement of +A and -A. This can be plotted using the wave equation y (x, t) = A sin (kx - ωt), where k is the wave number and ω is the angular frequency of the wave. The wave translates in the positive x-direction with a period T, which is the inverse of the frequency. The speed of the wave is computed by dividing the distance by the time taken, and the wavelength is given by the product of the speed and the period of the wave.

Understanding the Parameters

• The speed of the wave is how fast it propagates through the medium.
• The period of the wave, T, relates to the frequency at which the end of the string is moved.
• The wavelength is the distance over which the wave's shape repeats.
• Above parameters help in visualizing and graphing the motion on a plot of displacement versus time.

The graph would show a sine wave pattern with points moving to the maximum and minimum displacements representing the amplitude A.

Answer 2

The student is sending pulses of a transverse sinusoidal wave to the right along a string. The displacement of the wave can be plotted using a high-speed camera at regular intervals of the period.

Step-by-step explanation:

In the given scenario, the student is sending pulses of a transverse sinusoidal wave to the right along a string. The wave is modeled using the wave equation y(x, t) = A sin (6.00 m-¹x - 24.00 s¹t).

Since the wave is transverse, the displacement will oscillate up and down between y= +A and y= -A. Each point on the string will undergo simple harmonic motion with a period T.

The displacement of the wave at any point can be plotted over time using a high-speed camera, capturing snapshots at regular intervals of T.