### Waves - Result Question 8

#### 8. A transverse wave propagating along $x$-axis is represented by $y(x, t)=8.0 \sin (0.5 \pi x-4 \pi t-\frac{\pi}{4})$ where $x$ is in metres and $t$ is in seconds. The speed of the wave is

[2006]

(a) $0.5 \pi m / s$

(b) $\frac{\pi}{4} m / s$

(c) $8 m / s$

(d) $4 \pi m / s$

## Show Answer

#### Answer:

Correct Answer: 8. (c)

Solution:

- (c) Speed of a wave represented by the equation

$y(x, t)=A \sin (k x-\omega t+\phi)$ is $v=\frac{\omega}{k}$

By comparison, $\omega=4 \pi ; k=0.5 \pi$

$v=\frac{\omega}{k}=\frac{4 \pi}{0.5 \pi}=8 m / sec$