A standing wave on a string has the form: y(x,t) = (3.6 mm)sin[x/(3.6 m)]cos[(14

Question

A standing wave on a string has the form:
y(x,t) = (3.6 mm)sin[x/(3.6 m)]cos[(143.0 rad/s)t].

Two traveling waves combined to form this standing wave, one moving to the right (positive x-direction) and one moving to the left.
a. What is the amplitude of the right-moving wave?


b. What is the amplitude of the left-moving wave?


c. What is the wavelength of the right-moving wave?


d. What is the wavelength of the left-moving wave?


e. What is the speed of the right-moving wave?


f. What is the speed of the left-moving wave?

I really need well detailed naswer please
thanks

Explanation / Answer

given that standing wave equation is y(x,t) = (3.6 mm)sin[x/(3.6 m)]cos[(143.0 rad/s)t]. ......(1)

we need to compare this equation with resultant standing wave equation y( x,t) = (2 a sin kx) cos t ......(2) comparing equation (1) and (2)     2a = 3.00mm        a = 3.00 mm/2           = 1.5 mm here a is amplitude of right and left travelling wave a) amplitude of rigth moving wave a = 1.5 mm b) amplitude of left moving wave   a = 1.5 mm and also k = 1/ 3.6 m here       k = 2/                 2/ = 1/ 3.6 m                     = 2 ( 3.6 m)                         = 22.6 m so wave length of righ and left   travelling wave = 22.6 m angular frequency of the wave is = 143 .0 rad/s                                                     2f = 143 .0 rad/s                                                         f = 143 .0 rad/s/ 2                                                           = 22.77 Hz speed of the wave v = f                                    = ( 22.6 m) ( 22.77 Hz)                                    = 514.61 m/s so speed of the left and righ moving waves is 514.61 m/s

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