Question 496: 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

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