Ch 16 Waves and Sound

AP Learning Objectives WAVES AND OPTICS Wave motion (including sound) Traveling waves Students should understand the description of traveling waves, so they can: Sketch or identify graphs that represent traveling waves and determine the amplitude, wavelength, and frequency of a wave from such a graph. Apply the relation among wavelength, frequency, and velocity for a wave. Understand qualitatively the Doppler effect for sound in order to explain why there is a frequency shift in both the moving-source and moving-observer case. Describe reflection of a wave from the fixed or free end of a string. Describe qualitatively what factors determine the speed of waves on a string and the speed of sound.

AP Learning Objectives Wave propagation Students should understand the difference between transverse and longitudinal waves, and be able to explain qualitatively why transverse waves can exhibit polarization. Students should understand the inverse-square law, so they can calculate the intensity of waves at a given distance from a source of specified power and compare the intensities at different distances from the source.

Table of Contents The Nature of Waves Periodic Waves The Speed of a Wave on a String (AP?) The Mathematical Description of a Wave (AP?) The Nature of Sound The Speed of Sound (AP?) Sound Intensity (AP?) Decibels (AP?) The Doppler Effect Applications of Sound in Medicine (Not AP) The Sensitivity of the Human Ear (Not AP)

Chapter 16: Waves & Sounds Section 1: The Nature of Waves

Physics Models There are two common base models when trying to describe the physical world Particle A small point object, with mass, that can rotate and translate This is the model we’ve been using so far this year Wave The movement of energy through a collection of collection of point particles. (EM waves excluded)

Mechanical Waves A mechanical wave is a disturbance which propagates through a medium with little or no net displacement of the particles of the medium.

Types of Waves A transverse wave is a wave in which particles of the medium move in a direction perpendicular to the direction which the wave moves. Example: Waves on a String

Types of Waves A longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction which the wave moves. These are also called compression waves . Example: sound

Types of Waves Light: Electromagnetic (Discussed in Ch 24) Earthquakes/Ocean Waves: combination

Boundary Effects Wave Reflection Occurs when a wave strikes a medium boundary and “bounces back” into original medium. Completely reflected waves have the same energy and speed as original wave. Wave Refraction Transmission of wave from one medium to another. Refracted waves may change speed and wavelength. Refraction is almost always accompanied by some reflection. Refracted waves do not change frequency.

Types of Reflection Fixed-end reflection: The wave reflects with inverted phase. Open-end reflection: The wave reflects with the same phase Animations courtesy of Dr. Dan Russell, Kettering University

16.1.1. A transverse wave is traveling along a Slinky. The drawing below represents a section of the Slinky at one instant in time. The direction the wave is traveling is from left to right. Two segments are labeled on the Slinky. At the instant shown, which of the following statements correctly describes the motion of the particles that compose the Slinky in segments A and B? a) In segment A the particles are moving downward and in segment B the particles are moving upward. b) In segment A the particles are moving upward and in segment B the particles are moving upward. c) In segment A the particles are moving downward and in segment B the particles are moving downward. d) In segment A the particles are moving upward and in segment B the particles are moving downward. e) In segment A the particles are moving toward the left and in segment B the particles are moving toward the right.

16.1.2. Mike is holding one end of a Slinky. His hand moves up and down and causes a transverse wave to travel along the Slinky away from him. Is the motion of Mike’s hand a wave? a) Yes, the motion of Mike’s hand is a wave because it moves up and down in periodic motion. b) Yes, the motion of Mike’s hand is a wave because Mike is transferring energy to the Slinky. c) No, the motion of Mike’s hand is not a wave because there is no traveling disturbance. d) No, the motion of Mike’s hand is not a wave because there is no energy traveling along the Slinky.

Chapter 16: Waves & Sounds Section 2: Periodic Waves

Characteristic Wave Variables The amplitude (A) is the maximum excursion of a particle of the medium from the particles undisturbed position. The wavelength (  ) is the horizontal length of one cycle of the wave. The period (T) is the time required for one complete cycle. The frequency ( f or  in chem) is the number of cycles that pass a given point per unit of time is related to the period and has units of Hz, or s-1. In the drawing, one cycle is shaded in color.

Parts of a Wave Periodic waves consist of cycles or patterns that are produced over and over again by the source. In the figures, every segment of the slinky vibrates in simple harmonic motion, provided the end of the slinky is moved in simple harmonic motion.

Example 1 The Wavelengths of Radio Waves AM and FM radio waves are transverse waves consisting of electric and magnetic field disturbances traveling at a speed of 3.00x10 8 m/s. A station broadcasts AM radio waves whose frequency is 1230x10 3 Hz and an FM radio wave whose frequency is 91.9x10 6 Hz. Find the distance between adjacent crests in each wave. AM FM

16.2.1. Jimmy and Jenny are floating on a quiet river using giant doughnut-shaped tubes. At one point, they are 5.0 m apart when a speed boat passes. After the boat passes, they begin bobbing up and down at a frequency of 0.25 Hz. Just as Jenny reaches her highest level, Jimmy is at his lowest level. As it happens, Jenny and Jimmy are always within one wavelength. What is the speed of these waves? a) 1.3 m/s b) 2.5 m/s c) 3.8 m/s d) 5.0 m/s e) 7.5 m/s

16.2.2. The drawing shows the vertical position of points along a string versus distance as a wave travels along the string. Six points on the wave are labeled A, B, C, D, E, and F. Between which two points is the length of the segment equal to one wavelength? a) A to E b) B to D c) A to C d) A to F e) C to F

16.2.3. A longitudinal wave with an amplitude of 0.02 m moves horizontally along a Slinky with a speed of 2 m/s. Which one of the following statements concerning this wave is true? a) Each particle in the Slinky moves a distance of 2 m each second. b) Each particle in the Slinky moves a vertical distance of 0.04 m during each period of the wave. c) Each particle in the Slinky moves a horizontal distance of 0.04 m during each period of the wave. d) Each particle in the Slinky moves a vertical distance of 0.02 m during each period of the wave. e) Each particle in the Slinky has a wavelength of 0.04 m.

16.2.4. A sound wave is being emitted from a speaker with a frequency f and an amplitude A . The sound waves travel at a constant speed of 343 m/s in air. Which one of the following actions would reduce the wavelength of the sound waves to one half of their initial value? a) increase the frequency to 2 f b) increase the amplitude to 2 A c) decrease the frequency to f /4 d) decrease the frequency to f /2 e) decrease the amplitude to A /2

Problem: Sound travels at approximately 340 m/s, and light travels at 3.0 x 10 8 m/s. Approximately how far away is a lightning strike if the sound off the thunder arrives at a location 2.0 seconds after the lightning is seen? (Hint: assume light moves instantaneously)

Problem: The frequency of an oboe's A is 440 Hz. What is the period of this note? Assume a speed of sound in air of 340 m/s.

Problem: The frequency of an oboe's A is 440 Hz. What is the wavelength? Assume a speed of sound in air of 340 m/s.

Chapter 16: Waves & Sounds Section 3: The Speed of a Wave on a String (AP?)

Speed of a Wave in a String The speed at which the wave moves to the right depends on how quickly one particle of the string is accelerated upward in response to the net pulling force. tension linear density

Example 2 Waves Traveling on Guitar Strings Transverse waves travel on each string of an electric guitar after the string is plucked. The length of each string between its two fixed ends is 0.628 m, and the mass is 0.208 g for the highest pitched E string and 3.32 g for the lowest pitched E string. Each string is under a tension of 226 N. Find the speeds of the waves on the two strings. High E Low E

Conceptual Example 3 Wave Speed Versus Particle Speed Is the speed of a transverse wave on a string the same as the speed at which a particle on the string moves?

16.3.1. The tension of a guitar string in increased by a factor of 4. How does the speed of a wave on the string increase, if at all? a) The speed of a wave is reduced to one-fourth the value it had before the increase in tension. b) The speed of a wave is reduced to one-half the value it had before the increase in tension. c) The speed of a wave remains the same as before the increase in tension. d) The speed of a wave is increased to two times the value it had before the increase in tension. e) The speed of a wave is increased to four times the value it had before the increase in tension.

16.3.2. Two identical strings each have one end attached to a wall. The other ends are each attached to a separate spool that allows the tension of each string to be changed independently. Consider each of the waves shown. Which one of the following statements is true if the frequency and amplitude of the waves is the same? a) The tension in the string on which wave A is traveling is four times that in the string on which wave D is traveling. b) The tension in the string on which wave B is traveling is four times that in the string on which wave D is traveling. c) The tension in the string on which wave B is traveling is four times that in the string on which wave A is traveling. d) The tension in the string on which wave D is traveling is four times that in the string on which wave A is traveling. e) The tension in the string on which wave C is traveling is four times that in the string on which wave B is traveling.

16.3.3. A climbing rope is hanging from the ceiling in a gymnasium. A student grabs the end of the rope and begins moving it back and forth with a constant amplitude and frequency. A transverse wave moves up the rope. Which of the following statements describing the speed of the wave is true? a) The speed of the wave decreases as it moves upward. b) The speed of the wave increases as it moves upward. c) The speed of the wave is constant as it moves upward. d) The speed of the wave does not depend on the mass of the rope. e) The speed of the wave depends on its amplitude.

16.3.4. When a wire is stretched by a force F , the speed of a traveling wave is v . What is the speed of the wave on the wire when the force is doubled to 3 F ? a) v b) 3 v c) 9 v d) e)

Chapter 16: Waves & Sounds Section 4: The Mathematical Description of a Wave (AP?)

What is the displacement y at time t of a particle located at x ?

16.4.1. A radio station broadcasts its radio signal at a frequency of 101.5 MHz. The signals travel radially outward from a tower at the speed of light. Which one of the following equations represents this wave if t is expressed in seconds and x is expressed in meters? a) y = 150 sin[(6.377  10 8 ) t  (2.123) x ] b) y = 150 sin[(637.7) t  (2.961) x ] c) y = 150 sin[(6.283  10 6 ) t  (2.961  10 3 ) x ] d) y = 150 sin[(101.5  10 6 ) t  (2.961) x ] e) y = 150 sin[(101.5  10 6 ) t  (2.123) x ]

16.4.2. The equation for a certain wave is y = 4.0 sin [2  (2.5 t + 0.14 x )] where y and x are measured in meters and t is measured in seconds. What is the magnitude and direction of the velocity of this wave? a) 1.8 m/s in the + x direction b) 1.8 m/s in the  x direction c) 18 m/s in the  x direction d) 7.2 m/s in the + x direction e) 0.35 m/s in the  x direction

16.4.3. Which one of the following statements correctly describes the wave given as this equation: , where distances are measured in cm and time is measured in ms? The wave is traveling in the + x direction with an amplitude of 3 cm and a wavelength of  /2 cm. The wave is traveling in the + x direction with an amplitude of  4 cm and a wavelength of  cm. The wave is traveling in the + x direction with an amplitude of 3 cm and a wavelength of  cm. The wave is traveling in the + x direction with an amplitude of 2 cm and a wavelength of  cm. e) The wave is traveling in the + x direction with an amplitude of 6 cm and a wavelength of  /2 cm.

16.4.4. Which one of the following correctly describes a wave described by y = 2.0 sin(3.0 x  2.0 t ) where y and x are measured in meters and t is measured in seconds? a) The wave is traveling in the + x direction with a frequency 6  Hz and a wavelength 3  m. b) The wave is traveling in the  x direction with a frequency 4  Hz and a wavelength  / 3 m. c) The wave is traveling in the + x direction with a frequency  Hz and a wavelength 3  m. d) The wave is traveling in the  x direction with a frequency 4  Hz and a wavelength  m. e) The wave is traveling in the + x direction with a frequency 6  Hz and a wavelength  / 3 m.

Chapter 16: Waves & Sounds Section 5: The Nature of Sound

Sound is Sound is a longitudinal wave Sound travels through the air at approximately 340 m/s. It travels through other media as well, often much faster than that! Sound waves are started by vibration of some other material, which starts the air moving. Crest  Condensation Trough  Rarefaction Animation courtesy of Dr. Dan Russell, Kettering University

Sound waves in 2D Individual air molecules are not carried along with the wave.

The Frequency of a Sound Wave The frequency is the number of cycles per second. A sound with a single frequency is called a pure tone . The brain interprets the frequency in terms of the subjective quality called pitch .

The Pressure Amplitude of a Sound Wave Loudness is an attribute of a sound that depends primarily on the pressure amplitude of the wave. Frequency is also factor

Perception of Sound We hear a sound as “high” or “low” depending on its frequency or wavelength. Sounds with high frequencies sound high-pitched to our ears, and sounds with low frequencies sound low-pitched. The range of human hearing is from about 20 Hz to about 20,000 Hz. The amplitude of a sound's vibration is interpreted as its loudness. We measure the loudness (also called sound intensity) on the decibel scale, which is logarithmic. The decibel scale will be discussed in section 8

16.5.1. A particle of dust is floating in the air approximately one half meter in front of a speaker. The speaker is then turned on produces a constant pure tone as shown. The sound waves produced by the speaker travel horizontally. Which one of the following statements correctly describes the subsequent motion of the dust particle, if any? a) The particle of dust will oscillate left and right with a frequency of 226 Hz. b) The particle of dust will oscillate up and down with a frequency of 226 Hz. c) The particle of dust will be accelerated toward the right and continue moving in that direction. d) The particle of dust will move toward the right at constant velocity. e) The dust particle will remain motionless as it cannot be affected by sound waves.

16.5.2. While constructing a rail line in the 1800s, spikes were driven to attach the rails to cross ties with a sledge hammer. Consider the sound that is generated each time the hammer hits the spike. How does the frequency of the sound change, if at al, as the spike is driven into the tie? a) The frequency of the sound does not change as the spike is driven. b) The frequency of the sound decreases as the spike is driven. c) The frequency of the sound increases as the spike is driven.

Chapter 16: Waves & Sounds Section 6: The Speed of Sound (AP?)

Speed of Sound Sound travels through gases, liquids, and solids at considerably different speeds.

Speed of Sound In a gas, it is only when molecules collide that the condensations and rarefactions of a sound wave can move from place to place. Ideal Gas

Conceptual Example 5 Lightning, Thunder, and a General Rule There is a general rule for estimating how far away a thunderstorm is. After you see a flash of lighting, count off the seconds until the thunder is heard. Divide the number of seconds by five. The result gives the approximate distance (in miles) to the thunderstorm. Why does this rule work?

16.6.1. In a classroom demonstration, a physics professor breathes in a small amount of helium and begins to talk. The result is that the professor’s normally low, baritone voice sounds quite high pitched. Which one of the following statements best describes this phenomena? a) The presence of helium changes the speed of sound in the air in the room, causing all sounds to have higher frequencies. b) The professor played a trick on the class by tightening his vocal cords to produces higher frequencies in his throat and mouth than normal. The helium was only a distraction and had nothing to do with it. c) The helium significantly alters the vocal chords causing the wavelength of the sounds generated to decrease and thus the frequencies increase. d) The wavelength of the sound generated in the professor’s throat and mouth is only changed slightly, but since the speed of sound in helium is approximately 2.5 times larger than in air, therefore the frequencies generated are about 2.5 times higher.

16.6.2. The graph shows measured data for the speed of sound in water and the density of the water versus temperature. From the graph and your knowledge of the speed of sound in liquids, what can we infer about the bulk modulus of water in the temperature range from 0 to 100  C? a) The bulk modulus of water increases linearly with temperature. b) The bulk modulus of water decreases non-linearly with temperature. c) The bulk modulus of water is constant with increasing temperature. d) The bulk modulus of water increases non-linearly with increasing temperature. e) The bulk modulus of water increases with increasing temperature until it peaks around 60  C after which it slowly decreases.

16.6.3. Ethanol has a density of 659 kg/m 3 . If the speed of sound in ethanol is 1162 m/s, what is its adiabatic bulk modulus? a) 1.7  10 8 N/m 2 b) 2.2  10 8 N/m 2 c) 7.7  10 8 N/m 2 d) 8.9  10 8 N/m 2 e) 6.1  10 9 N/m 2

Chapter 16: Waves & Sounds Section 7: Sound Intensity (AP?)

Sound Intensity Sound waves carry energy that can be used to do work. The amount of energy transported per second is called the power of the wave. The sound intensity is defined as the power that passes perpendicularly through a surface divided by the area of that surface.

Example 6 Sound Intensities 12x10 -5 W of sound power passed through the surfaces labeled 1 and 2. The areas of these surfaces are 4.0m 2 and 12m 2 . Determine the sound intensity at each surface.

Perception of Intensity For a 1000 Hz tone, the smallest sound intensity that the human ear can detect is about 1x10 -12 W/m 2 . This intensity is called the threshold of hearing . On the other extreme, continuous exposure to intensities greater than 1W/m 2 can be painful. If the source emits sound uniformly in all directions, the intensity depends on the distance from the source in a simple way.

Sound Power power of sound source area of sphere

Conceptual Example 8 Reflected Sound and Sound Intensity Suppose the person singing in the shower produces a sound power P. Sound reflects from the surrounding shower stall. At a distance r in front of the person, does the equation for the intensity of sound emitted uniformly in all directions underestimate, overestimate, or give the correct sound intensity?

16.7.1. Natalie is a distance d in front of a speaker emitting sound waves. She then moves to a position that is a distance 2 d in front of the speaker. By what percentage does the sound intensity decrease for Natalie between the two positions? a) 10 % b) 25 % c) 50 % d) 75% e) The sound intensity remains constant because it is not dependent on the distance.

16.7.2. A bell is ringing inside of a sealed glass jar that is connected to a vacuum pump. Initially, the jar is filled with air at atmospheric pressure. What does one hear as the air is slowly removed from the jar by the pump? a) The sound intensity gradually increases. b) The sound intensity gradually decreases. c) The sound intensity of the bell does not change. d) The frequency of the sound gradually increases. e) The frequency of the sound gradually decreases.

Chapter 16: Waves & Sounds Section 8: Decibels (AP?)

The Decibel Scale The decibel (dB) is a measurement unit used when comparing two sound intensities. Because of the way in which the human hearing mechanism responds to intensity, it is appropriate to use a logarithmic scale called the intensity level: Note that log(1)=0, so when the intensity of the sound is equal to the threshold of hearing, the intensity level is zero.

Example 9 Comparing Sound Intensities Audio system 1 produces a sound intensity level of 90.0 dB, and system 2 produces an intensity level of 93.0 dB. Determine the ratio of intensities.

16.8.1. A sound level meter is used measure the sound intensity level. A sound level meter is placed an equal distance in front of two speakers, one to the left and one to the right. A signal of constant frequency may be sent to each of the speakers independently or at the same time. When either the left speaker is turned on or the right speaker is turned on, the sound level meter reads 90.0 dB. What will the sound level meter read when both speakers are turned on at the same time? a) 90.0 dB b) 93.0 dB c) 96.0 dB d) 100.0 dB e) 180.0 dB

16.8.2. A sound level meter is used measure the sound intensity level. A sound level meter is placed an equal distance in front of two speakers, one to the left and one to the right. A signal of constant frequency, but differing amplitude, is sent to each speaker independently. When the left speaker is turned on the sound level meter reads 85 dB. When the right speaker is turned on the sound level meter reads 65 dB. What will the sound level meter read when both speakers are turned on at the same time? a) about 85 dB b) about 65 dB c) about 150 dB d) about 75 dB e) about 113 dB

16.8.3. Software is used to amplify a digital sound file on a computer by 20 dB. By what factor has the intensity of the sound been increased as compared to the original sound file? a) 2 b) 5 c) 10 d) 20 e) 100

Chapter 16: Waves & Sounds Section 9: The Doppler Effect

The Doppler Effect The Doppler Effect is the perceived change in frequency (pitch) of a sound detected by an observer because the sound source and the observer have different velocities with respect to the medium of sound propagation. When a car blowing its horn races toward you, the sound of its horn appears higher in pitch, since the wavelength has been effectively shortened by the motion of the car relative to you. The opposite happens when the car races away

The Doppler Effect Stationary source Subsonic source Source breaking sound barrier Supersonic source Animations courtesy of Dr. Dan Russell, Kettering University

Doppler Effect – Moving Source

Doppler Effect source moving toward a stationary observer source moving away from a stationary observer

Example 10 The Sound of a Passing Train A high-speed train is traveling at a speed of 44.7 m/s when the engineer sounds the 415-Hz warning horn. The speed of sound is 343 m/s. What are the frequency and wavelength of the sound, as perceived by a person standing at the crossing, when the train is (a) approaching and (b) leaving the crossing? approaching leaving

Doppler Effect – Moving Observer

Doppler Effect – Moving Observer Observer moving towards stationary source Observer moving away from stationary source

General Doppler Equation Numerator: plus sign applies when observer moves towards the source Denominator: minus sign applies when source moves towards the observer

16.9.1. Two stationary observers, Keisha and Trina, are listening to the sound from a moving source. The sound from the source has a constant frequency f S and constant amplitude. As the source moves, Trina hears two different frequencies f 1 and f 2 , where f 1 > f S and f 2 < f S . Keisha, who is not moving with the source, only hears one frequency, f . Which one of the following statements best explains this situation?. a) The source is moving very slowly relative to Keisha, but fast relative to Trina. b) The source is moving along a parabolic path and Keisha is at the origin of the parabola. Trina is inside the parabola. c) Keisha is standing at a location where the wind is blowing in such a way as to remove the Doppler effect, while Trina is standing in a location where there is no wind. d) The source is moving along a circle and Keisha is at the center of the circle. Trina is outside the circle. e) The source is moving along an ellipse and Keisha is at one of the two foci of the ellipse. Trina is outside the ellipse.

16.9.2. A child is swinging back and forth with a constant period and amplitude. Somewhere in front of the child, a stationary horn is emitting a constant tone of frequency f S . Five points are labeled in the drawing to indicate positions along the arc as the child swings. At which position(s) will the child hear the lowest frequency for the sound from the whistle? a) at B when moving toward A b) at B when moving toward C c) at C when moving toward B d) at C when moving toward D e) at both A and D

16.9.3. Hydrogen atoms in a distant galaxy are observed to emit light that is shifted to lower frequencies with respect to hydrogen atoms here on Earth. Astronomers use this information to determine the relative velocity of the galaxy with respect to the Earth by observing how light emitted by atoms is Doppler shifted. For the hydrogen atoms mentioned, how are the wavelengths of light affected by the relative motion, if at all? a) The wavelengths would be unchanged, only the frequencies are shifted. b) The wavelengths of light would be longer than those observed on Earth. c) The wavelengths of light would be shorter than those observed on Earth.

Chapter 16: Waves & Sounds Section 10: Applications of Sound in Medicine (Not AP)

Applications of Sound in Medicine By scanning ultrasonic waves across the body and detecting the echoes from various locations, it is possible to obtain an image.

Applications of Sound in Medicine Ultrasonic sound waves cause the tip of the probe to vibrate at 23 kHz and shatter sections of the tumor that it touches.

Applications of Sound in Medicine When the sound is reflected from the red blood cells, its frequency is changed in a kind of Doppler effect because the cells are moving.

Chapter 16: Waves & Sound Section 11: The Sensitivity of the Human Ear (Not AP)

The Sensitivity of the Human Ear

Ch 16 Waves and Sound

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