Physics 2A Chapters 16: Waves and Sound We are what we believe we are. Benjamin Cardozo We would accomplish many more things if we did not think of them as impossible C. Malesherbez The only limit to our realization of tomorrow will be our doubts of today. Let us move forward with strong and active faith. Franklin Delano Roosevelt Reading: pages 422 447 (skip sections 16.4 and16.6) Outline: introduction to waves transverse and longitudinal waves general description of waves amplitude, wavelength, period, frequency, and wave speed the speed of a wave on a string the nature of sound (PowerPoint) sound intensity decibels the Doppler effect Problem Solving Many of the problems involving waves on a string deal with the relationships v = λ f = λ /T, where v is the wave speed, λ is the wavelength, f is the frequency, and T is the period. Typical problems might give you the wavelength and frequency, then ask for the wave speed, or might give you the wave speed and period, then ask for the wavelength. Sometimes the quantities are given by describing the motion. For example, a problem might tell you that the string at one point takes a certain time to go from its equilibrium position to maximum displacement. This, of course, is one-fourth the period. In other problems, you may be asked how long it takes a particle on a string to move through a total distance. You must then recognize that a particle on the string moves through a distance a 4A (where A is the amplitude) during a time equal to the period. Some problems deal with the wave speed. For waves on a string, the fundamental equation is v= F/( m/ L), where F is the tension in the string and m and L are the mass and length of the string. The tension may not be given directly but, if the problem asks for the wave speed, sufficient information will be given to calculate it.
Nearly all Doppler shift problems can be solved using f 0 v0 1± f v = s v s 1 v where v is speed of sound, v S is the speed of the source, v o is the speed of the observer, f s is the frequency of the source, and f o is the frequency detected by the observer. The upper sign in the numerator refers to a situation in which the observer is moving toward the source; the lower sign refers to a situation in which the observer is moving away from the source. The upper sign in the denominator refers to a situation in which the source is moving toward the observer; the lower sign refers to a situation in which the source is moving away from the observer. Remember that all speeds are measured relative to the medium in which the sound is propagating. You might be given the velocities and one of the frequencies, then asked for the other frequency. In other situations you might be given the two frequencies and one of the velocities, then asked for the other velocity. In all cases, simple algebraic manipulation of the equation will produce the desired expression. Questions and Example Problems from Chapter 16 Question 1 A loudspeaker produces a sound wave. Does the wavelength of the sound increase, decrease, or remain the same, when the wave travels from air into water? Justify your answer. Question 2 Two cars, one behind the other, are traveling in the same direction at the same speed. Does either driver hear the other s horn at a frequency that is different from that heard when both cars are at rest?
Problem 1 Light is an electromagnetic wave and travels at a speed of 3.00 10 8 m/s. The human eye is most sensitive to yellow-green light, which has a wavelength of 5.45 10-7 m. What is the frequency of this light? Problem 2 A longitudinal wave with a frequency of 3.0 Hz takes 1.7 s to travel the length of a 2.5 m Slinky. Determine the wavelength of the wave.
Problem 3 A brother and sister try to communicate with a string ties between to tin cans. If the string is 9.5 m long, has a mass of 32 g, and is pulled taut with a tension of 8.6 N, how long does it take to travel from one end of the string to the other? Problem 4 A stretched string has a mass per unit length of 5.00 g/cm and a tension of 10.0 N. A wave on this string has an amplitude of 0.12 mm and a frequency of 100.00 Hz. What is the wavelength of the wave?
Problem 5 A loudspeaker has circular opening with a radius of 0.0950 m. The electrical power needed to operate the speaker is 25.0 W. The average sound intensity at the opening is 17.5 W/m 2. What percentage of the electrical power is converted by the speaker into sound power? Problem 6 The average sound intensity inside a busy restaurant is 3.2 10-5 W/m 2. How much energy goes into each ear (area = 2.1 10-3 m 2 ) during a one hour meal?
Problem 7 When a person wears a hearing aid, the sound intensity level increases by 30.0 db. By what factor does the sound intensity increase? Problem 8 A recording engineer works in a soundproofed room that is 44.0 db quieter than the outside. If the sound intensity in the room is 1.20 10-10 W/m 2, what is the intensity outside?
Problem 9 The security alarm on a parked car goes off and produces a frequency of 960 Hz. The speed of sound is 343 m/s. As you drive toward this parked car, pass it, and drive away, you observe the frequency to change by 95 Hz. At what speed are you driving? Problem 10 In the figure below, a French submarine and a U.S. submarine move toward each other during maneuvers in motionless water in the North Atlantic. The French sub moves at speed v F = 50.00 km/h, and the U.S. sub at v US = 70.00 km/h. The French sub sends out a sonar signal (sound wave in water) at 1.00 10 3 Hz. Sonar waves travel at 5470 km/h. (a) What is the signal s frequency as detected by the U.S. sub? (b) What frequency is detected by the French sub in the signal reflected back to it by the U.S. sub?