The wave described by y=0.25 (10 π x-2 π t) , where x and y are in metre and t in second, is a wave travelling along the

NEET 2008

NEET 2008 · Physics · Waves and Sound

The wave described by y=0.25 (10 π x-2 π t) , where x and y are in...

The wave described by

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

, where

x

and

y

are in metre and

t

in second, is a wave travelling along the

A- ve $x$ direction with frequency $1 \mathrm{~Hz}$
B+ve $x$ direction with frequency $\pi \mathrm{Hz}$ and wavelength $\lambda=0.2 \mathrm{~m}$
C+ ve $x$ direction with frequency $1 \mathrm{~Hz}$ and wavelength $\lambda=0.2 \mathrm{~m}$
D-ve $x$ direction with amplitude $0.25 \mathrm{~m}$ and wavelength $\lambda=0.2 \mathrm{~m}$

C. + ve $x$ direction with frequency $1 \mathrm{~Hz}$ and wavelength $\lambda=0.2 \mathrm{~m}$

Key Idea : The sign between two terms in argument of sine will define its direction. Writing the given wave equation

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

The minus

(-)

between

(10 \pi x)

and

(2 \pi t)

implies that the wave is travelling along positive

x

direction. Now comparing Eq. (i) with standard wave equation

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

We have

\begin{array}{l} a=0.25 \mathrm{~m}, \omega=2 \pi, k=10 \pi \mathrm{m} \\ \therefore \frac{2 \pi}{T}=2 \pi \\ \Rightarrow f=1 \mathrm{~Hz} \end{array}

Also,

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

Therefore, the wave is travelling along +ve

x

direction with frequency

1 \mathrm{~Hz}

and wavelength

0.2 \mathrm{~m}