Two graphs are obtained for a transverse pulse on a taut rope

PHYSICS · Multi-part · CBSE · Physics · Waves · Waves

Problem

Two graphs are obtained for a transverse pulse on a taut rope. • Graph A: The displacement

y

at the fixed position

x = 0

is recorded as a function of time. The first four successive crests occur at times

2.0\,\text{ms}

6.0\,\text{ms}

10.0\,\text{ms}

, and

14.0\,\text{ms}

. Each crest reaches a height of

+0.35\,\text{m}

, and each trough reaches

-0.35\,\text{m}

. • Graph B: At the instant

t = 0

, the displacement along the rope is recorded as a function of position

x

. Crests are found at

x = 1.2\,\text{m}

x = 5.6\,\text{m}

, and

x = 10.0\,\text{m}

, while troughs are midway between consecutive crests. Assume the rope has negligible damping and the wave is perfectly periodic. (a) Determine the amplitude

A

of the wave and cite specific evidence from the data that supports your answer. (b) Using Graph A, calculate the period

T

of the wave. Justify any averaging procedure you employ. (c) Using Graph B, calculate the wavelength

\lambda

of the wave and discuss any uncertainty in your measurement based on the data given. (d) Compute the speed

v

of the wave by combining your results from parts (b) and (c). Show the complete chain of reasoning. (e) Given that the first crest in Graph A occurs at

t = 2.0\,\text{ms}

but the first crest in Graph B is located at

x = 1.2\,\text{m}

, deduce the direction in which the wave is propagating along the rope. Explain your logic clearly.

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