# Warm-Up Exercise 15

## Due 12:15 pm, Mon 1 Oct 2012

Physics 123, Fall 2012

Suppose you create a pulse by moving the free end of a taut string up and down once with your hand beginning at t=0. The string is attached at its other end to a distant wall. The pulse reaches the wall at time tw. Which of the following, taken by itself, will decrease the time interval required for the center of the pulse to reach the wall? More than one choice may be correct. Mark all that apply
☐ Moving your hand up and down more quickly but by the same amount
☐ Moving your hand up and down more slowly but by the same amount
☐ Moving your hand the same speed but farther up and down
☐ Moving your hand the same speed but a shorter distance up and down
☐ Using a heavier string of the same length under the same tension
☑ Using a lighter string of the same length under the same tension
☑ Using the same string of the same length but under more tension
☐ Using the same string of the same length but under less tension

Explain how each of the following (keeping everything else the same) would impact the energy transfer rate of a wave on a string:
A) reducing the mass density of the string
B) doubling the wavelength
C) doubling the tension
D) doubling the amplitude

Recall that P=1/2 μω^2A^2v A] reduces the power (linearly), assuming that the velocity is unchanged B] irrelevant to rate of energy transfer C] increasing tension increases velocity and therefore power (in a sqrt(tension) fashion) D] increases the rate of energy transfer a lot (quadratically)