Wave described by y = 0.25,sin ,left( {10π x - 2π t} right) , where x and y are in meters an

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14.Waves and Sound

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The wave described by $y = 0.25\,\sin \,\left( {10\pi x - 2\pi t} \right)$ , where $x$ and $y$ are in $meters$ and $t$ in $seconds$ , is a wave travelling along is

A

$+ve$ $x$ direction with frequency $1\, Hz$ and wavelength $\lambda = 0.2\,m$.

B

$-ve$ $x$ direction with amplitude $0.25\, m$ and wavelength $\lambda = 0.2\,m$.

C

$-ve$ $x$ direction with frequency $1\, Hz.$

D

$+ve$ $x$ direction with frequency $\pi\, Hz$ and wavelength $\lambda = 0.2\,m$

Solution

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

$\mathrm{y}_{\max. }=0.25$

$\mathrm{k}=\frac{2 \pi}{\lambda}=10 \pi$ or $\lambda=0.2 \mathrm{m}$

$\omega=2 \pi \mathrm{f}=2 \pi$

or $\mathrm{f}=1 \mathrm{\,Hz}$

The sign is negative inside the bracket.

Therefore, this wave travels in the positive $X -$ direction.

Standard 11

Physics

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