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Question

A sinusoidal wave propagates along a string in figure (a) and (b). 'y' represents displacement of particle from the mean position. 'x' & 't' have usual meanings. Find:

1. Wavelength, frequency and speed of the wave

2. Maximum velocity and maximum acceleration of the particles


A

2m, 0.25 Hz, 2 ms-1, 1.5 mms-1, 0.75 mms-2

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B

4m, 0.25 Hz, 10 ms-1, 1.5 πmms-1, 0.75 mms-2

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C

4m, 0.25 Hz, 1 ms-1, 1.5 π mms-1, 0.75 π2 mms-2

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D

None of these

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Solution

The correct option is C

4m, 0.25 Hz, 1 ms-1, 1.5 π mms-1, 0.75 π2 mms-2


From the y-t graph we can see the wave repeats itself on interval of 4s. So the time period is 4s. from the y-x graph we see that the distance between the points after which the wave repeats itself is 4m. Hence the wave length is 4m.

f=1T=14S1=0.25s1

v=λf=414=1 ms1

vp max=Aω

=A×(2πf

=3××2π×0.25 [A=3 from y vst graph]

apmax=ω2A

=(2π×0.25)2×3

34π2=0.075 π2mms2


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