A stretched string is set into transverse sinusoidal motion

PHYSICS · Multi-part · A Level · Physics · Waves · Waves

Problem

A stretched string is set into transverse sinusoidal motion. A student records two separate graphs of the same disturbance. • Graph 1 ("history graph"): The vertical displacement

y

of a single point on the string located at

x=0

is plotted versus time

t

. The graph shows regularly spaced peaks of equal height. Peak heights reach

+3.0\,\text{cm}

and troughs reach

-3.0\,\text{cm}

. The first peak occurs at

t=1.6\,\text{ms}

, the next peak at

t=5.0\,\text{ms}

, and the following peak at

t=8.4\,\text{ms}

. • Graph 2 ("snapshot graph"): At an instant

t=0

, the vertical displacement

y

along the string is plotted versus position

x

. The graph shows a repeating pattern of crests and troughs of the same amplitude as in Graph 1. Successive crests are located at

x=0.12\,\text{m}

x=0.46\,\text{m}

, and

x=0.80\,\text{m}

. Assume the wave is sinusoidal, continuous, and travels without damping. (a) Describe qualitatively how Graph 1 allows one to identify the physical quantity called the period

T

and how Graph 2 allows one to identify the physical quantity called the wavelength

\lambda

. In your description, state precisely what features of each graph correspond to these quantities. (b) Using the numerical data provided, determine the period

T

of the wave. Show reasoning that justifies your use of the data. (c) Using the numerical data provided, determine the wavelength

\lambda

of the wave. Explain any assumptions you make about the spacing of the crests. (d) Explain how the amplitude

A

of the wave is obtained from either graph and state its value. (e) Discuss why the amplitude is independent of the period and wavelength for this wave, referring to evidence in the graphs.

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