A transverse wave on a string travelling along +ve x-axis has been shown in the figure below:
The mathematical form of the shown wave is $y = (3 .0 cm) \sin [2 π \times 0 .1 t - \frac{2 π}{100} x]$
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.

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738 cm, in upward direction

6 cm, in upward direction

732 cm, in upward direction

6 cm, in downward direction

answer is C.

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Detailed Solution

At the moment shown in the figure, particle at 1 is moving in the downward direction.
We have, T = 1/0.1 s = 10s.
In one complete cycle, particle travels a distance, 4 times the amplitude. So, in time 10 min 15 s, i.e., 615 s which means 61 full + t half cycles, the distance travelled

$= (4 \times 3) \times 61 + (2 \times 3) \times 1 = 732 + 6 = 738 cm$