An harmonic wave has been set up on a very long string which travels along the length of the string. The wave has a frequency of 50 Hz, amplitude 1 cm and wavelength 0.5 m. find
(a) the time taken by the wave to travel a distance of 8 m along the length of string (b) the time taken by a point on the string to travel a distance of 8 m, once the wave has reached the point and sets it into motion (c ) also. consider the above case when the amplitude gets doubled

Explanation

The wave is travelling along the length of string, while points on the string are moving perpendicular to the length of the 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, time period.
`T=(1)/(f)=(1)/(50)s=0.02s`
And wave speed, `v=flambda=50xx0.5=25 m//s`
(a) Time taken by wave to travel a distance of `8 m,t_(1)=8//25 s`
(b) Time taken by a point on string to travel a distance of `8 m`,
`t_(2)=(8)/(4A)xxT=(8)/(4xx10^(-2))xx0.02=4 s`
(c ) when the amplitude gets doubled, the answer (c ) for (a). does not change.
For (b),
`t_(2)=(8)/(4A)xxT=(8)/(4xx2A)xx0.02=2 s`