A wave represented by the given equation Y = A ( 10 , ,x + 15 , ,… - Vidyadip

MCQ

A wave represented by the given equation $Y = A\sin \left( {10\,\pi \,x + 15\,\pi \,t + \frac{\pi }{3}} \right)$, where $x$ is in meter and $t$ is in second. The expression represents

A
A wave travelling in the positive $X$ direction with a velocity of $1.5 \,m/sec$
B
A wave travelling in the negative $X$ direction with a velocity of $1.5\, m/sec$
C
A wave travelling in the negative $ X$ direction with a wavelength of $ 0.2\, m$
✓
Both $(b)$ and $(c)$

✓

Answer

Correct option: D.

Both $(b)$ and $(c)$

d
(d) Standard wave equation which travel in negative $x-$ direction is $y = A\sin (\omega \,t + kx + {\varphi _0})$

For the given wave $\omega = 2\pi n = 15\pi ,\,\,k = \frac{{2\pi }}{\lambda } = 10\pi $

Now $v = \frac{{{\rm{Co - efficient \,of\, }}t}}{{{\rm{Co - efficient \,of \,}}x}}$ $ = \frac{\omega }{k} = \frac{{15\pi }}{{10\pi }} = 1.5\,m/sec$

and $\lambda = \frac{{2\pi }}{k} = \frac{{2\pi }}{{10\pi }} = 0.2\,m.$

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