4. Wave Equation Below is a snapshot graph at D(m) t=0 s of a 5.0 Hz wave travel

Question

4. Wave Equation Below is a snapshot graph at D(m) t=0 s of a 5.0 Hz wave traveling to the left. (a) What is the wave speed? (b) What is the phase constant of the wave? (c) Write the displacement equation for this wave. x (m) 5. Speed of Propagation vs. Particle Speed (a) Show that )-Acos(kx-or) may be written as v(x,r)-Acosx) Snapshot graph at 0s 2 (b) Use n to find an expression for the transverse velocity vy, of a particle in the string on which the wave travels. (c) Find the maximum speed of a particle of the string. Under what circumstances is this equal to the propagation speed v? Less than v? Greater than v?

Explanation / Answer

4. (A) wavelength = 2 m

v = wavelength f = 2 x 5 = 10 m/s

(B) cos(phi) = 0.5

phi = pi/3 rad

(C) x = A cos(k x - w t + phi )

x = (1 mm) cos[ pi x - 10 pi t + pi / 3]

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