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

Answer 1

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, $v=f\lambda =25m/s$
Time taken by wave to travel a distance of 8 m,
$t_1=\frac{8}{25}s=0.32s$
Time taken by particle on string to travel a distance of 8 m,
$t_2=\frac{8\times T}{4timesamplitude}=\frac{8}{4\times 0.01}\times 0.02=4s$