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(C) The standard equation for a progressive wave is $x = A \sin(\omega t + ky)$.Comparing the given equation $x = 1.2 \sin(314t + 12.56y)$ with the st

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$0.5 \, m, -ve \, y$-direction

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(C) The standard equation for a progressive wave is $x = A \sin(\omega t + ky)$.Comparing the given equation $x = 1.2 \sin(314t + 12.56y)$ with the standard form,we get the wave number $k = 12.56 \, 	ext{rad/m}$.The wavelength $\lambda$ is given by the formula $\lambda = \frac{2\pi}{k}$.Substituting the value of $k$ and $\pi \approx 3.14$:$\lambda = \frac{2 	imes 3.14}{12.56} = \frac{6.28}{12.56} = 0.5 \, 	ext{m}$.Since the term inside the sine function is $(314t + 12.56y)$,the positive sign between the $t$ and $y$ terms indicates that the wave is traveling in the negative direction of the axis associated with the variable $y$.Therefore,the wave is traveling in the $-ve \, y$-direction.

The equation of a progressive wave is given by $x = 1.2 \sin(314t + 12.56y)$. What are the wavelength and the direction of the wave?

Similar Questions

The equation of a plane progressive wave is given by $y = 5 \cos \pi (200t - \frac{x}{150})$ where $x$ and $y$ are in cm and $t$ is in second. The velocity of the wave is . . . . . . m/s.

What is a progressive wave?

In the given progressive wave $y = 5 \sin(100\pi t + 0.4\pi x)$,where $y$ and $x$ are in $m$ and $t$ is in $s$. Find the:
$(a)$ Amplitude
$(b)$ Wavelength
$(c)$ Frequency
$(d)$ Wave velocity
$(e)$ Particle velocity amplitude.

Among the following,the equation representing a progressive wave is
$(A)$ $y=2 \cos 3x \sin 10t$
$(B)$ $y=2 \sqrt{x-vt}$
$(C)$ $y=3 \sin (5x-0.5t)+4 \cos (5x-0.5t)$
$(D)$ $y=\cos x \sin t+\cos 2x \sin 2t$

$A$ progressive wave moving along the $x$-axis is represented by $y = A \sin \left[ \frac{2 \pi}{\lambda} (vt - x) \right]$. The wavelength $\lambda$ at which the maximum particle velocity is $3$ times the wave velocity is:

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