Section 15.7 The Doppler Effect and Shock Waves (cont.) © 2015 Pearson Education, Inc.

Sound Waves from a Moving Source (Review) The frequency f+ = v/λ+ detected by the observer whom the source is approaching is higher than the frequency emitted by the source. The observer behind the source detects a lower frequency than the source emits. The Doppler effect is the change in frequency when a source moves relative to an observer. © 2015 Pearson Education, Inc.

Example 15.13 How fast are the police driving? A police siren has a frequency of 550 Hz as the police car approaches you, 450 Hz after it has passed you and is moving away. How fast are the police traveling? © 2015 Pearson Education, Inc.

Example 15.13 How fast are the police driving? (cont.) A police siren has a frequency of 550 Hz as the police car approaches you, 450 Hz after it has passed you and is moving away. How fast are the police traveling? prepare The siren’s frequency is altered by the Doppler effect. The frequency is f+ as the car approaches and f− as it moves away. We can write two equations for these frequencies and solve for the speed of the police car, vs. © 2015 Pearson Education, Inc.

Example 15.13 How fast are the police driving? (cont.) solve Because our goal is to find vs, we rewrite Equations 15.16 as Subtracting the second equation from the first, we get © 2015 Pearson Education, Inc.

Example 15.13 How fast are the police driving? (cont.) Now we can solve for the speed vs: assess This is pretty fast (about 75 mph) but reasonable for a police car speeding with the siren on. © 2015 Pearson Education, Inc.

A Stationary Source and a Moving Observer The frequency heard by a moving observer depends on whether the observer is approaching or receding from the source: © 2015 Pearson Education, Inc.

The Doppler Effect for Light Waves If the source of light is receding from you, the wavelength you detect is longer than that emitted by the source. The light is shifted toward the red end of the visible spectrum; this effect is called the red shift. The light you detect from a source moving toward you is blue shifted to shorter wavelengths. © 2015 Pearson Education, Inc.

The Doppler Effect for Light Waves All distant galaxies are redshifted, so all galaxies are moving away from us. Extrapolating backward brings us to a time where all matter in the universe began rushing out of a primordial fireball in an event known as the Big Bang. Measurements show the universe began 14 billion years ago. © 2015 Pearson Education, Inc.

Frequency Shift on Reflection from a Moving Object A wave striking a barrier or obstacle can reflect and travel back to the source. For sound, this is an echo. For an object moving toward a source, it will detect a frequency Doppler shifted to a higher frequency. The wave reflected back will again be Doppler shifted since the object (where reflection occurred) is approaching the source. © 2015 Pearson Education, Inc.

Frequency Shift on Reflection from a Moving Object Thus, the echo from a moving object is “double Doppler shifted.” The frequency shift of reflected waves is A Doppler ultrasound can detect not only structure but also motion. © 2015 Pearson Education, Inc.

Example 15.14 The Doppler blood flowmeter If an ultrasound source is pressed against the skin, the sound waves reflect off tissues in the body. Some of the sound waves reflect from blood cells moving through arteries toward or away from the source, producing a frequency shift in the reflected wave. A biomedical engineer is designing a Doppler blood flowmeter to measure blood flow in an artery where a typical flow speed is known to be 0.60 m/s. What ultrasound frequency should she use to produce a frequency shift of 1500 Hz when this flow is detected? © 2015 Pearson Education, Inc.

Example 15.14 The Doppler blood flowmeter (cont.) solve We can rewrite Equation 15.18 to calculate the frequency of the emitter: The values on the right side are all known. Thus the required ultrasound frequency is assess Doppler units to measure blood flow in deep tissues actually work at about 2.0 MHz, so our answer is reasonable. © 2015 Pearson Education, Inc.

Shock Waves A shock wave is produced when a source moves faster than the waves, which causes waves to overlap. The overlapping waves add up to a large amplitude wave, which is the shock wave. © 2015 Pearson Education, Inc.

Shock Waves A source is supersonic if it travels faster than the speed of sound. A shock wave travels with the source. If a supersonic source passes an observer, the shock wave produces a sonic boom. Less extreme examples of shock waves include the wake of a boat and the crack of a whip. © 2015 Pearson Education, Inc.

Example Problem A Doppler ultrasound is used to measure the motion of blood in a patient’s artery. The probe has a frequency of 5.0 MHz, and the maximum frequency shift on reflection is 400 Hz. What is the maximum speed of the blood in the artery? Answer: Using eq. 15.18 with the speed of sound in human tissue (1540 m/s) from table 15.1 we have v = 0.5*400/(5E6)*1540 = 0.062 m/s = 6.2 cm/s. © 2015 Pearson Education, Inc.

© 2015 Pearson Education, Inc.

Chapter 16 Superposition and Standing Waves Chapter Goal: To use the idea of superposition to understand the phenomena of interference and standing waves. © 2015 Pearson Education, Inc.

Chapter 16 Preview Looking Ahead: Superposition Where the two water waves meet, the motion of the water is a sum, a superposition, of the waves. You’ll learn how this interference can be constructive or destructive, leading to larger or smaller amplitudes. © 2015 Pearson Education, Inc.

Chapter 16 Preview Looking Ahead: Standing Waves The superposition of waves on a string can lead to a wave that oscillates in place—a standing wave. You’ll learn the patterns of standing waves on strings and standing sound waves in tubes. © 2015 Pearson Education, Inc.

Chapter 16 Preview Looking Ahead: Speech and Hearing Changing the shape of your mouth alters the pattern of standing sound waves in your vocal tract. You’ll learn how your vocal tract produces, and your ear interprets, different mixes of waves. © 2015 Pearson Education, Inc.

Chapter 16 Preview Looking Back: Traveling Waves In Chapter 15 you learned the properties of traveling waves and relationships among the variables that describe them. In this chapter, you’ll extend the analysis to understand the interference of waves and the properties of standing waves. © 2015 Pearson Education, Inc.

Chapter 16 Preview Stop to Think A 170 Hz sound wave in air has a wavelength of 2.0 m. The frequency is now doubled to 340 Hz. What is the new wavelength? 4.0 m 3.0 m 2.0 m 1.0 m Stop to Think Answer: D © 2015 Pearson Education, Inc.

Chapter 16 Preview Stop to Think A 170 Hz sound wave in air has a wavelength of 2.0 m. The frequency is now doubled to 340 Hz. What is the new wavelength? 4.0 m 3.0 m 2.0 m 1.0 m Stop to Think Answer: D © 2015 Pearson Education, Inc.

Section 16.1 The Principle of Superposition © 2015 Pearson Education, Inc.

The Principle of Superposition If two baseballs are thrown across the same point at the same time, the balls will hit one another and be deflected. © 2015 Pearson Education, Inc.

The Principle of Superposition Waves, however, can pass through one another. Both observers would hear undistorted sound, despite the sound waves crossing. © 2015 Pearson Education, Inc.

The Principle of Superposition © 2015 Pearson Education, Inc.

The Principle of Superposition To use the principle of superposition, you must know the displacement that each wave would cause if it were alone in the medium. Then you must go through the medium point by point and add the displacements due to each wave at that point. © 2015 Pearson Education, Inc.

Constructive and Destructive Interference The superposition of two waves is called interference. Constructive interference occurs when both waves are positive and the total displacement of the medium is larger than it would be for either wave separately. © 2015 Pearson Education, Inc.

Constructive and Destructive Interference The superposition of two waves is called interference. Constructive interference occurs when both waves are positive and the total displacement of the medium is larger than it would be for either wave separately. © 2015 Pearson Education, Inc.

Constructive and Destructive Interference Destructive interference is when the displacement of the medium where the waves overlap is less than it would be due to either of the waves separately. During destructive interference, the energy of the wave is in the form of kinetic energy of the medium. © 2015 Pearson Education, Inc.

Constructive and Destructive Interference Destructive interference is when the displacement of the medium where the waves overlap is less than it would be due to either of the waves separately. During destructive interference, the energy of the wave is in the form of kinetic energy of the medium. © 2015 Pearson Education, Inc.

Constructive and Destructive Interference Destructive interference is when the displacement of the medium where the waves overlap is less than it would be due to either of the waves separately. During destructive interference, the energy of the wave is in the form of kinetic energy of the medium. © 2015 Pearson Education, Inc.

QuickCheck 16.1 Two wave pulses on a string approach each other at speeds of 1 m/s. How does the string look at t = 3 s? Answer: C © 2015 Pearson Education, Inc. 35

QuickCheck 16.1 Two wave pulses on a string approach each other at speeds of 1 m/s. How does the string look at t = 3 s? C. © 2015 Pearson Education, Inc. 36

QuickCheck 16.2 Two wave pulses on a string approach each other at speeds of 1 m/s. How does the string look at t = 3 s? Answer: B © 2015 Pearson Education, Inc. 37

QuickCheck 16.2 Two wave pulses on a string approach each other at speeds of 1 m/s. How does the string look at t = 3 s? B. © 2015 Pearson Education, Inc. 38

QuickCheck 16.3 Two waves on a string are moving toward each other. A picture at t = 0 s appears as follows: How does the string appear at t = 2 s? Answer: A © 2015 Pearson Education, Inc.

QuickCheck 16.3 Two waves on a string are moving toward each other. A picture at t = 0 s appears as follows: How does the string appear at t = 2 s? A. © 2015 Pearson Education, Inc.

Section 16.2 Standing Waves © 2015 Pearson Education, Inc.

Standing Waves Waves that are “trapped” and cannot travel in either direction are called standing waves. Individual points on a string oscillate up and down, but the wave itself does not travel. It is called a standing wave because the crests and troughs “stand in place” as it oscillates. © 2015 Pearson Education, Inc.

Superposition Creates a Standing Wave As two sinusoidal waves of equal wavelength and amplitude travel in opposite directions along a string, superposition will occur when the waves interact. In the following slides, the two waves are represented by red and orange, respectively. At each point, the net displacement of the medium is found by adding the red displacement and the orange displacement. The blue wave is the resulting wave due to superposition. © 2015 Pearson Education, Inc.

Superposition Creates a Standing Wave © 2015 Pearson Education, Inc.

Superposition Creates a Standing Wave © 2015 Pearson Education, Inc.

Superposition Creates a Standing Wave © 2015 Pearson Education, Inc.

Nodes and Antinodes In a standing wave pattern, there are some points that never move. These points are called nodes and are spaced λ/2 apart. Antinodes are halfway between the nodes, where the particles in the medium oscillate with maximum displacement. © 2015 Pearson Education, Inc.

Nodes and Antinodes The wavelength of a standing wave is twice the distance between successive nodes or antinodes. At the nodes, the displacement of the two waves cancel one another by destructive interference. The particles in the medium at a node have no motion. © 2015 Pearson Education, Inc.

Nodes and Antinodes At the antinodes, the two waves have equal magnitude and the same sign, so constructive interference at these points give a displacement twice that of the individual waves. The intensity is maximum at points of constructive interference and zero at points of destructive interference. © 2015 Pearson Education, Inc.

QuickCheck 16.4 What is the wavelength of this standing wave? 0.25 m Standing waves don’t have a wavelength. Answer: C © 2015 Pearson Education, Inc. 50

QuickCheck 16.4 What is the wavelength of this standing wave? 0.25 m Standing waves don’t have a wavelength. © 2015 Pearson Education, Inc. 51