Question 457: Waves

Question

A wave travelling in the + ve x-direction having displacement along  y-direction as 1 m, wavelength 2$\pi $ m and frequency of ${1 \over \pi }$ Hz is represented by

Accepted Answer

The standard equation of a wave travelling along +ve x-direction is given by
${m{y  =  Asin(kx - }}\omega {m{t)}}$
where A = Amplitude of the wave
k = angular wave number
$\omega $ = angular frequency of the wave
Given: A = 1 m, $\lambda  = {m{2}}\pi m,\upsilon  = {1 \over \pi }Hz$
As $k = {{2\pi } \over \lambda } = {{2\pi } \over {2\pi }} = 1$
$\omega  = 2\pi \upsilon  = 2\pi  	imes {1 \over \pi } = 2$
$ 	herefore $ The equation of the given wave is
y = 1 sin (1x Ã¢ÂÂ 2t) = sin(x Ã¢ÂÂ 2t)

Answer

y = sin(10$\pi $x $-$ 20$\pi $t)

Answer

y = sin(2$\pi $x + 2$\pi $t)

Answer

y = sin(x $-$ 2t)

Answer

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

Waves

A wave travelling in the + ve x-direction having displacement along y-direction as 1 m, wavelength 2\pi m and frequency of {1 \over \pi } Hz is represented by

Choose the correct answer: