A transverse sinusoidal wave on a string has a period T = 41.0 ms and travels in

Question

A transverse sinusoidal wave on a string has a period T = 41.0 ms and travels in the negative x direction with a speed of 30.0 m/s. At t = 0, a particle on the string at x = 0 has a transverse position of 2.00 cm and is traveling downward with a speed of 1.00 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

a)
y(x,t) = Asin(kx+wt+ )
y(0,0) = Asin(k*0+w*0+ ) = Asin
dy/dt = Awcos = -1.0 m/s
w = 2pi/T = 2pi/0.0410s = 48.780pi/s
A^2 = xi^2 + vi/w^2 = 0.020m^2+ (1.0m/s/48.780pi/s)^2
A = 0.0210 m = 2.103 *10^-2 m

b)
Asin/Acos = 0.020 / (-1.0/48.780pi) = -3.064 = tan
= - 71.924 o

c) vymax = Aw
=2.103 *10^-2 * 48.780pi/s

= 3.222 m/s

d) wave function of the wave : .0210 sin(kx + 153.2 t  - 71.924 )

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