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Question

A harmonic wave has been set up on a very long string which travels along the length of string. The wave has frequency of 50 Hz, amplitude 1 cm and wavelength 0.5 m. For the above described wave.
Statement I: Time taken by wave to travel a distance of 8 m along the length of string is 0.32 s.
Statement II: Time taken by a point on the string to travel a distance of 8 m, once the wave has reached at that point and sets it into motion is 0.32 s.

A
Both the statements are correct
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B
Statement I is correct but Statement II is incorrect
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C
Statement I is incorrect but Statement II is correct.
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D
Both the statements are incorrect.
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Solution

The correct option is B Statement I is correct but Statement II is incorrect
The wave is travelling along the length of a string while particles constituting the string are oscillation in a direction perpendicular to the length to string. In one time period (cycle), the wave moves forward
by one wavelength while the particle on string travels a distance of 4 times the amplitude.
Here, \(T = \frac{1}{f} = 0.02~s\)
Wave speed, v=fλ=25m/s
Time taken by wave to travel a distance of 8 m,
t1=825s=0.32 s
Time taken by particle on string to travel a distance of 8 m,
t2=8×T4 times amplitude=84×0.01×0.02=4s

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