A transverse sinusoidal wave is moving along a string in the positive direction

Question

A transverse sinusoidal wave is moving along a string in the positive direction of an x axis with a speed of 82 m/s. At t = 0, the string particle at x = 0 has a displacement of 4.0 cm from its equilibrium position and is not moving. The maximum transverse speed of the string particle at x = 0 is 20 m/s. (a) what is the frequency of the wave? (b) what is the wavelength of the wave? If the wave equation is of the form y(x, t) = y_m sin(kx plusminus omega t + psi), what are (c) y_m (d) k, (e) omega, (f) psi, and (g) the correct choice of sign in front of omega? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units (f) Number Units (g)

Explanation / Answer

A) maximum transverse speed = Ym*w

20 = 0.04*2pi*f

f = 20/(0.04*2pi)

= 79.6 Hz

B) wavelength = v/f

= 82/79.6

= 1.03 m

C) ym = 0.04 m

D) k = 1/wavelength = 0.971 per m

E) w= 2pi f = 500 rad/s

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