Question

A vibrating tuning fork generates a wave given by y=0.1 sin π(0.1x-2t),where x and y are in metre and t is in second.The distance travelled by the wave while the fork completes 30 vibrations is:
a)600m b)36m c)20m d)200m

Answer 1

Answer on Question#38255 - Physics - Other

$$y = 0.1 \sin \pi (0.1x - 2t)$$

First let's choose a fixed $x = x_0$ and find the period $T$ for $t$ of the wave. Since the sine function has a period of $2\pi$ so:

$$\pi (0.1x_0 - 2t) - \pi (0.1x_0 - 2t_0) = 2\pi$$ $$2\pi T = 2\pi$$ $$T = 1 \text{ second}$$

So the period is 1 second; 30 seconds needed to make 30 vibrations.

Now let's discuss how the peek ($y_{max} = 0.1$) moves along the x-axis.

When $t = 0$ the peek is at $x = 5$ because $y_{max} = 0.1 = y(5,0) = 0.1\sin \pi (0.1\cdot 5)$.

When $t = 30$ we have:

$$\pi (0.1x - 2 \cdot 30) = \frac{\pi}{2}$$ $$0.1x - 60 = 0.5$$ $$x - 600 = 5$$ $$x = 605$$

So at $t = 30$ the peek is at $x = 605$ and we get that the wave covers $605 - 5 = 600$ meters.

ANSWER: A