Dr. Jie ZouPHY Chapter 16 Wave Motion (Cont.)

Dr. Jie ZouPHY Outline Reflection and Transmission Rate of energy transfer by sinusoidal waves on strings (derivation)

Dr. Jie ZouPHY Reflection The reflection of a traveling wave pulse at the fixed end of a stretched string. The reflected pulse is inverted, but its shape is unchanged. The reflection of a traveling wave pulse at the free end of a stretched string. The reflected pulse is NOT inverted.

Dr. Jie ZouPHY Transmission A pulse traveling to the right on a light string attached to a heavier string. Part of the incident pulse is reflected (and inverted), and part is transmitted to the heavier string. A pulse traveling to the right on a heavier string attached to a lighter string. The incident pulse is partially reflected (not inverted) and partially transmitted.

Dr. Jie ZouPHY Rate of energy transfer by sinusoidal waves on strings As waves propagate through a medium, they transport energy. The total potential energy in one wavelength U = (1/4)   2 A 2 The total kinetic energy in one wavelength K =(1/4)   2 A 2 The total energy in one wavelength of the wave E = U + K =(1/2)   2 A 2 The power (the rate of energy transfer) = E /  t =(1/2)   2 A 2 /T=(1/2)   2 A 2 v The rate of energy transfer in any sinusoidal wave is proportional to the square of the angular frequency and to the square of the amplitude. See detailed derivations on the textbook.

Dr. Jie ZouPHY Example 16.6 A taut string for which  = 5.00 x kg/m is under a tension of 80.0 N. (a) How much power must be supplied to the string to generate sinusoidal waves at a frequency of 60.0 Hz and an amplitude of 6.00 cm? (b) What if the string is to transfer energy at a rate of 1000 W? What must be the required amplitude if all other parameters remain the same?

Dr. Jie ZouPHY Homework Ch. 16, P. 508, Problems: #34, 40.