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 $\lambda=0.2 m$
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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.
