Dr. Jie Zou PHY 1151G Department of Physics Chapter 14 Waves and Sound (Cont.) Dr. Jie Zou PHY 1151G Department of Physics

Dr. Jie Zou PHY 1151G Department of Physics Outline Standing waves Standing waves on a string Vibrating columns of air Sound intensity Doppler effect Moving observer Moving source Dr. Jie Zou PHY 1151G Department of Physics

Dr. Jie Zou PHY 1151G Department of Physics A standing wave A standing wave is one that oscillates with time, but remains fixed in its location. It is in this sense that the wave is said to be “standing”. Example: (a) A string tied down at both ends; (b) When plucked in the middle, a standing wave results-the fundamental mode of oscillation of the string. 1 = 2L (wavelength of the fundamental) Dr. Jie Zou PHY 1151G Department of Physics

Standing waves on a string Antinode (A) Standing waves on a string Node (N) First harmonic (fundamental) frequency and wavelength: f1 = v/(2L); 1 = 2L v = (F/)1/2: wave speed on the string; F: tension in the string; : mass per unit length of the string; L: length of the string Frequency and wavelength of the nth harmonic, with n = 1, 2, 3,…: fn = nf1 = ; n = 1/n = 2L/n Dr. Jie Zou PHY 1151G Department of Physics

An application – guitar Dr. Jie Zou PHY 1151G Department of Physics

Vibrating columns of air Standing waves in a column of air closed at one end: f1 = v/(4L); fn = nf1 = , n = 1, 3, 5,… odd harmonics only n = 1/n = 4L/n v: speed of sound in air L: length of the air column Dr. Jie Zou PHY 1151G Department of Physics

Dr. Jie Zou PHY 1151G Department of Physics Example An empty soda pop bottle is to be used as a musical instrument in a band. In order to be tuned properly, the fundamental frequency of the bottle must be 440.0 Hz. (a) If the bottle is 26.0 cm tall, how high should it be filled with water to produce the desired frequency? Treat the bottle as a pipe that is closed at one end (the surface of the water) and open at the other end. (6.5 cm) (b) What is the frequency of the next higher harmonic for this bottle? (1320 Hz) Dr. Jie Zou PHY 1151G Department of Physics

Dr. Jie Zou PHY 1151G Department of Physics Sound intensity The loudness of a sound is determined by its intensity. Definition of intensity: If the energy E passes through the area A in the time t, the intensity, I, of the wave is I = E/(At). Since the power P = E/t, I = P/A. SI unit: W/m2. The intensity falls off with the square of the distance: I = P/(4r2). SI unit: W/m2. Dr. Jie Zou PHY 1151G Department of Physics

Example: Intensity of sound Two people relaxing on a deck listen to a songbird sing. One person, only 1.00 m from the bird, hears the sound with an intensity of 2.80 10-6 W/m2 . What intensity is heard by the second person, who is 4.25 m from the bird? Assume that no reflected sound is heard by either person. Dr. Jie Zou PHY 1151G Department of Physics

Dr. Jie Zou PHY 1151G Department of Physics Doppler effect Doppler effect: The change in pitch, due to the relative motion between a source of sound and the receiver, is called the Doppler effect. The pitch increases when the observer and the source are moving closer together. The pitch decreases when the observer and source are separating. Dr. Jie Zou PHY 1151G Department of Physics

Doppler effect for a moving observer For moving observer: f´= (1  u/v)f f´= frequency to the observer. f = frequency of the source of the sound. u = speed of the observer. v = speed of the sound. “+”: when the observer moves toward the source. “-”: when the observer moves away from the source. Dr. Jie Zou PHY 1151G Department of Physics

Doppler effect for a moving source For moving source: f’ = [1/(1  u/v)] f u = speed of the source. v = speed of the sound. “-”: when the source moves toward the observer. “+”: when the source moves away from the observer. Dr. Jie Zou PHY 1151G Department of Physics

Example: Doppler effect A train sounds its whistle as it approaches a tunnel in a cliff. The whistle produces a tone of 650.0 Hz, and the train travels with a speed of 21.2 m/s. (a) Find the frequency heard by an observer standing near the tunnel entrance. (b) The sound from the whistle reflects from the cliff back to the engineer in the train. What frequency does the engineer hear? Dr. Jie Zou PHY 1151G Department of Physics

Dr. Jie Zou PHY 1151G Department of Physics Homework See online homework assignment on www.masteringphysics.com Dr. Jie Zou PHY 1151G Department of Physics