(B) The general equation for a wave traveling in the negative $x$-direction is given by $y(x, t) = A \sin(kx + \omega t + \phi)$ or $A \cos(kx + \omeg

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$y(x, t) = 0.5\cos(2\pi x + 4\pi t)$

(B) The general equation for a wave traveling in the negative $x$-direction is given by $y(x, t) = A \sin(kx + \omega t + \phi)$ or $A \cos(kx + \omega t + \phi)$.Given: Amplitude $A = 0.5\, m$,Wavelength $\lambda = 1\, m$,Frequency $f = 2\, Hz$.Calculate the angular wave number $k = \frac{2\pi}{\lambda} = \frac{2\pi}{1} = 2\pi\, rad/m$.Calculate the angular frequency $\omega = 2\pi f = 2\pi(2) = 4\pi\, rad/s$.Substituting these values into the wave equation: $y(x, t) = 0.5 \cos(2\pi x + 4\pi t)$.Thus,option $B$ is correct.

Class 11 Physics Waves and Sound Wave Equation and Characteristics of Waves

Easy

$A$ transverse wave of amplitude $0.5\, m$,wavelength $1\, m$,and frequency $2\, Hz$ is propagating in a string in the negative $x$-direction. The expression for this wave is:

AIIMS 1980 All AIIMS

A
$y(x, t) = 0.5\sin(2\pi x - 4\pi t)$
B
$y(x, t) = 0.5\cos(2\pi x + 4\pi t)$
C
$y(x, t) = 0.5\sin(\pi x - 2\pi t)$
D
$y(x, t) = 0.5\cos(2\pi x + 2\pi t)$

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Wave Equation and Characteristics of Waves

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MediumAIPMT 2006

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$A$ transverse wave of amplitude $0.5\, m$,wavelength $1\, m$,and frequency $2\, Hz$ is propagating in a string in the negative $x$-direction. The expression for this wave is:

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$A$ sound wave of frequency $245 \,Hz$ travels with the speed of $300 \,ms^{-1}$ along the positive $x$-axis. Each point of the wave moves to and fro through a total distance of $6 \,cm$. What will be the mathematical expression of this travelling wave?

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