A transverse wave on a string travelling along + ve x-axis has been shown in the figure below:
The mathmetical form of the shown wave is
`y=(3.0 cm) sin [2pixx0.1t-(2pi)/(100)x]`
where t is in seconds and x is in centimetres. Find the total distance travelled by the particle at (1) in 10 min 15 s. measured from the instant shown in the figure and direction of its motion at the end of this time.

Options

A. 6 cm, in upward direction
B. 6 cm, in downward directiion
C. 738 cm, in upward direction
D. 732 cm, in upward direction

Answer

c

Explanation

At the moment shown in the figure, particle at `1` is moving in the downward direction.
we have, `T=1//0.1 s=10 s`.
in one complete cycle, particle travels a distance, `4` times the amplitude. So, in time `10` min `10 s`, i.e., `615 s` which means 61 full `+ 1` half cycles, hte distance travelled
`=(4xx3)xx61+(2xx3)xx1=732+6=738 cm`
At time instant, the particle is moving in the upward direction.