### Waves - Result Question 6

#### 6. The wave described by $y=0.25 \sin (10 \pi x-$ $2 \pi t$ ), where $x$ and $y$ are in meters and $t$ in seconds, is a wave travelling along the:

(a) -ve $x$ direction with frequency $1 Hz$.

[2008]

(b) +ve $x$ direction with frequency $\pi Hz$ and wavelength $\lambda=0.2 m$.

(c) +ve $x$ direction with frequency $1 Hz$ and wavelength $\lambda=0.2 m$

(d) -ve $x$ direction with amplitude $0.25 m$ and wavelength $\lambda=0.2 m$

## Show Answer

#### Answer:

Correct Answer: 6. (c)

Solution:

- (c) $y=0.25 \sin (10 \pi x-2 \pi t)$

Comparing this equation with the standard wave equation

$y=a \sin (k x-\omega t)$

We get, $k=10 \pi$

$\Rightarrow \frac{2 \pi}{\lambda}=10 \pi \Rightarrow \lambda=0.2 m$

And $\omega=2 \pi$ or, $2 \pi v=2 \pi \Rightarrow v=1 Hz$.

The sign inside the bracket is negative, hence the wave travels in +ve $x$-direction.