Chapter 19: Problem 8

Question: The equation of a transverse wave traveling along a string is given by , where x and y are in meters and t is in seconds. Find

1. The amplitude of the wave.
2. The frequency of the wave.
3. The velocity of the wave.
4. The wavelength of the wave.
5. The maximum transverse speed of a particle on the string.

Solution: We determine these quantities by comparing with the expression we have for a sine wave traveling in the positive x-direction, . We see that the amplitude , , and . This tells us that , , and .

For a particle undergoing simple harmonic motion, its maximum speed is and therefore we have .