A transverse sinusoidal wave on a string has a period T = 23.0 ms and travels in

Question

A transverse sinusoidal wave on a string has a period T = 23.0 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 2.50 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

w = 2pi/T = 2pi/0.023 = 273.18 rad/s

k = w/v = 273.18/30 = 9.106 m^-1

y = 0.022*sin(9.106x +8273.18t + phi)

particle speed = v = w*sqrt(A^2-y^2)

2.5 = 273.18*sqrt(A^2-0.02^2)

A = 0.022 m

A = 2.2 cm

--

at t = 0

x = 0

b)

y = 2 cm

2 = 2.2*sin(phi)

phi = 1.14 rad

c)

Vmax = A*w = 0.022*273.18 = 6.01 m/s

D)

y = 0.022*sin(9.106x +8273.18t + 1.14)

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