A transverse sinusoidal wave on a string has a period T = 35.0 ms and travels in

Question

A transverse sinusoidal wave on a string has a period T = 35.0 ms and travels in the negative x direction with a speed of 30.0 m/s. At t = 0, a particle on the string atx = 0 has a transverse position of 2.00 cm and is traveling downward with a speed of 5.50 m/s.

(a) What is the amplitude of the wave?
m

(b) What is the phase constant?
rad

(c) What is the maximum transverse speed of the string?
m/s

(d) Write the wave function for the wave. (Use the form Asin(kx + t + ). Round all coefficients to three significant figures.)
y(x, t) =  

Explanation / Answer

the transverse position of and velocity of the particle is

y = A cos ( wt+ kx + phi)

dy/ dt = wA sin ( wt+ kx + phi)

(b)

phase constant is

phi = tan^-1 ( v/ wy)

= tan^-1 ( 5.5 m/s/( 2 pi/0.035 s) ( 0.02 m)

= 0.99 rad

(a)

amplitude of the wave is

A = y/ cos phi = 2.0 cm/ cos 0.99 = 3.64 cm

(c)

maximu speed is

v = A w = ( 0.0364 m) ( 2 pi/ 0.035 s) = 6.53 m/s

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