Superposition Question

timtng

A transverse wave of frequency 40 Hz
propagates down a string. Two points 5 cm apart are
out of phase by p/6. (a) What is the wavelength of the
wave? (b) At a given point, what is the phase
difference between two displacements for times 5 ms
apart? (c) What is the wave velocity?

for a.) I use theta=(sπx)/λ
solving for λ I get λ=.6m

Please help me on part b and c, and check to see if I did part a correctly.

chroot

For part b, you can figure out the phase difference by looking at the frequency of the wave. The frequency is 40 Hz, so the wave has a period T = 1/40 Hz = 0.025 s. The time period 50 ms is thus 0.050 / 0.025 = 2 periods, exactly. If the point on the string executes exactly an integer number of periods in 50 ms, then its phase difference between the beginning and end of that 50 ms period is zero.

For part c, you know the frequency, 40 Hz, and the wavelength, 0.6 m. You can find the velocity with

[tex]v = \lambda \cdot \nu[/tex]

Does this make sense?

- Warren