A transverse sinusoidal wave on a string has a period T = 25.0 ms and travels in

Question

A transverse sinusoidal wave on a string has a period T = 25.0 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 travelling downward with a speed of 5.50 m/s. (a) what is the amplitude of the wave? m (b) What is the phase content? 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 + omegat + phi). Round all coefficients to three significant figures.)

Explanation / Answer

time period T = 25 ms

w = 2pi/T = 251.33 rad/s

v = 30 m/s = lambda/T

wavelength lambda = 30*0.025 = 0.75 m

speed of particel v = w*sqrt(A^2-y^2) = 5.5

(a)

w*sqrt(A^2-y^2) = 5.5

252.33*sqrt(A^2-0.02^2) = 5.5

A = 2.96 cm <<-----answer

(b)

y = A*sin(kx+wt+phi)

at t = 0

x = 0

y = 2 cm

2 = 2.96*sinphi

phi = 0.742

(c)

Vmax = A*w = 251.33*0.03 = 7.54 m/s

(d)

k = w/v = 2pi/Tv = (2pi)/(0.025*30) = 8.38 /m

y(x,t) = 0.03*sin(8.38x + 251.33t + 0.742)

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