The transverse displacement of points on a long string at the instant is recorded in…

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

Problem

The transverse displacement

y

of points on a long string at the instant

t = 0

is recorded in the table below. x (cm):

0\quad 6.25\quad 12.5\quad 18.75\quad 25\quad 31.25\quad 37.5\quad 43.75\quad 50

y (cm):

0\quad 1.414\quad 2.00\quad 1.414\quad 0\quad -1.414\quad -2.00\quad -1.414\quad 0

(a) Plot a smooth graph of

y

versus

x

for the range

0 \le x \le 50\,\text{cm}

and hence obtain the amplitude and wavelength of the wave. (b) A fixed point on the string at

x = 0

returns to its maximum positive displacement again at

t = 0.010\,\text{s}

. Determine the time period and frequency of the wave. (c) Using the values obtained in parts (a) and (b), calculate the speed of the wave along the string. (d) Sketch on the same set of axes the expected displacement–position graph after an additional time interval of

0.005\,\text{s}

, indicating clearly how the waveform has shifted.

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