Chapter 16 Waves and Sound 16.1 The Nature of Waves 1. A wave is a traveling disturbance. 2. A wave carries energy from place to place. 1
16.1 The Nature of Waves Transverse Wave 16.1 The Nature of Waves Longitudinal Wave 2
16.1 The Nature of Waves Water waves are partially transverse and partially longitudinal. 16.2 Periodic Waves 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. 3
16.2 Periodic Waves In the drawing, one cycle is shaded in color. The amplitude A is the maximum excursion of a particle of the medium from the particles undisturbed position. The wavelength (λ) is the horizontal length of one cycle of the wave. The period (T) is the time required for one complete cycle. The frequency (f) is related to the period and has units of Hz, or s -1. f 1 T v T f What is the frequency of the wave in the graph? Given that the wavelength of the wave is 20cm, what is the velocity of the wave? T 4.1s 3.3s 0.8sec 1 1 f 1.25Hz T 0.8 v f (1.25Hz)(0.20m) v 0.25m / s 4
16.2 Periodic Waves 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 f v 8 3.0010 m s 3 123010 Hz 244 m FM f v 8 3.0010 m s 3.26 m 6 91.910 Hz 16.3 The Speed of a Wave on 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. v F m L tension linear density 5
16.3 The Speed of a Wave on a String 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 v F m L 226 N 3 0.208 10 kg 0.628 m - 826m s Low E v F m L 226 N 3 3.32 10 kg 0.628 m - 207 m s 16.3 The Speed of a Wave on a String 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? 6
16.4 The Mathematical Description of a Wave What is the displacement y at time t of a particle located at x? 16.5 The Nature of Sound Waves LONGITUDINAL SOUND WAVES 7
16.5 The Nature of Sound Waves The distance between adjacent condensations is equal to the wavelength of the sound wave. 16.5 The Nature of Sound Waves Individual air molecules are not carried along with the wave. 8
16.5 The Nature of Sound Waves 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. 16.5 The Nature of Sound Waves THE PRESSURE AMPLITUDE OF A SOUND WAVE Loudness is an attribute of a sound that depends primarily on the pressure amplitude of the wave. 9
16.6 The Speed of Sound Sound travels through gases, liquids, and solids at considerably different speeds. Always remember, sound moves faster through solids 16.6 The Speed of Sound In a gas, it is only when molecules collide that the condensations and rerefactions of a sound wave can move from place to place. 3kT v rms m Ideal Gas v kt m k 1.3810 5 3 or 23 J K 7 5 10
16.6 The Speed of Sound Conceptual Example 5 Lightning, Thunder, and a Rule of Thumb There is a rule of thumb 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 The Speed of Sound LIQUIDS SOLID BARS v B ad v Y 11
Assignment pg. 501 #4,8,14,17,19,32,36,45,51 Chapter 16 Waves and Sound 12
16.7 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. I P A 16.7 Sound Intensity 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. I 1210 W 5 5 2 1 3.010 W m 2 1 4.0m A P I 1210 W 5 5 2 2 1.010 W m 2 2 12m A P 13
16.7 Sound 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. 16.7 Sound Intensity power of sound source I P 4 r 2 area of sphere 14
16.7 Sound Intensity 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? I P 4 r 2 16.8 Decibels 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: I 10 dblog I o I o 1.0010 12 W m 2 Note that log(1)=0, so when the intensity of the sound is equal to the threshold of hearing, the intensity level is zero. 15
16.8 Decibels I 10 dblog I o I o 1.0010 12 W m 2 16.8 Decibels 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. I 10 dblog I o 16
16.8 Decibels I 10 dblog I o I 1 1 10 db log I o 2 10 db log I o I 2 I I I I I 2 1 log 2 1 2 o 2 10 dblog 10 dblog 10 dblog 10 db I o Io I1 Io I1 3.0 db I 2 10 dblog I1 I 0.30 log I 2 1 I I 2 10 0. 30 1 2.0 16.9 The Doppler Effect The Doppler effect is the change in frequency or pitch of the sound detected by an observer because the sound source and the observer have different velocities with respect to the medium of sound propagation. 17
18 16.9 The Doppler Effect MOVING SOURCE v s T s s s s o f v f v v T v v v f v v f f s s o 1 1 16.9 The Doppler Effect v v f f s s o 1 1 source moving toward a stationary observer source moving away from a stationary observer v v f f s s o 1 1
16.9 The Doppler Effect 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? 1 1 f f f o s o fs 1 vs v 1 vs v f o approaching 1 1 415 Hz 477 Hz 44.7m s 343m s f o leaving 1 1 415 Hz 367 Hz 44.7m s 343m s 16.9 The Doppler Effect MOVING OBSERVER f o f s v o f s 1 v o fs v o fs 1 v 19
16.9 The Doppler Effect Observer moving towards stationary source v o fo fs 1 v Observer moving away from stationary source v o fo fs 1 v 16.9 The Doppler Effect GENERAL CASE f o v o 1 f v s vs 1 v Numerator: plus sign applies when observer moves towards the source Denominator: minus sign applies when source moves towards the observer 20
16.10 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. 16.10 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. 21
16.10 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. 16.11 The Sensitivity of the Human Ear 22
Assignment pg. 503-505 #52,54,60,64,68,71,78,80,82 Chapter 17 The Principle of Linear Superposition and Interference Phenomena 23
17.1 The Principle of Linear Superposition THE PRINCIPLE OF LINEAR SUPERPOSITION When two or more waves are present simultaneously at the same place, the resultant disturbance is the sum of the disturbances from the individual waves. 17.2 Constructive and Destructive Interference of Sound Waves When two waves always meet condensation-to-condensation and rarefaction-to-rarefaction, they are said to be exactly in phase and to exhibit constructive interference. 24
17.2 Constructive and Destructive Interference of Sound Waves When two waves always meet condensation-to-rarefaction, they are said to be exactly out of phase and to exhibit destructive interference. 17.2 Constructive and Destructive Interference of Sound Waves When two waves always meet condensation-to-rarefaction, they are said to be exactly out of phase and to exhibit destructive interference. This concept is used in noise cancelling headphones. The powered headphones create sound waves that are out of phase of the surrounding noise in order to cancel that sound out. 25
17.2 Constructive and Destructive Interference of Sound Waves If the wave patters do not shift relative to one another as time passes, the sources are said to be coherent. For two wave sources vibrating in phase, a difference in path lengths that is zero or an integer number (1, 2, 3,.. ) of wavelengths leads to constructive interference; a difference in path lengths that is a half-integer number (½, 1 ½, 2 ½,..) of wavelengths leads to destructive interference. 17.2 Constructive and Destructive Interference of Sound Waves Example 1 What Does a Listener Hear? Two in-phase loudspeakers, A and B, are separated by 3.20 m. A listener is stationed at C, which is 2.40 m in front of speaker B. Both speakers are playing identical 214-Hz tones, and the speed of sound is 343 m/s. Does the listener hear a loud sound, or no sound? 26
17.2 Constructive and Destructive Interference of Sound Waves Calculate the path length difference. 2 2 3.20 m 2.40 m 2.40 m 1.60 m Calculate the wavelength. v f 343m s 1.60 m 214 Hz Because the path length difference is equal to an integer (1) number of wavelengths, there is constructive interference, which means there is a loud sound. 17.3 Diffraction The bending of a wave around an obstacle or the edges of an opening is called diffraction. 27
17.3 Diffraction single slit first minimum Circular opening first minimum sin D sin 1. 22 D 17.3 Diffraction v f 343m s 1500 Hz 0.229 m 0.229m sin 1.22.9313 0.30m 1 o sin (.9313) 68 v f 343m s 8500 Hz 0.0404 m 0.0404m sin 1.22.1643 0.30m 1 o sin (.1643) 9.4 28
Assignment pg. 528-529 #2,5,7,9,10,12,18 17.4 Beats Two overlapping waves with slightly different frequencies gives rise to the phenomena of beats. 29
17.4 Beats The beat frequency is the difference between the two sound frequencies. 17.5 Transverse Standing Waves Transverse standing wave patters. 30
17.5 Transverse Standing Waves In reflecting from the wall, a forward-traveling halfcycle becomes a backward-traveling half-cycle that is inverted. Unless the timing is right, the newly formed and reflected cycles tend to offset one another. Repeated reinforcement between newly created and reflected cycles causes a large amplitude standing wave to develop. 17.5 Transverse Standing Waves String fixed at both ends f n v n 2L n 1,2,3,4, 31
17.5 Transverse Standing Waves f n v n 2L n 1,2,3,4, 17.5 Transverse Standing Waves Conceptual Example 5 The Frets on a Guitar Frets allow a the player to produce a complete sequence of musical notes on a single string. Starting with the fret at the top of the neck, each successive fret shows where the player should press to get the next note in the sequence. Musicians call the sequence the chromatic scale, and every thirteenth note in it corresponds to one octave, or a doubling of the sound frequency. The spacing between the frets is greatest at the top of the neck and decreases with each additional fret further on down. Why does the spacing decrease going down the neck? 32
17.6 Longitudinal Standing Waves A longitudinal standing wave pattern on a slinky. 17.6 Longitudinal Standing Waves Tube open at both ends f n v n 2L n 1,2,3,4, 33
17.6 Longitudinal Standing Waves Example 6 Playing a Flute When all the holes are closed on one type of flute, the lowest note it can sound is middle C (261.6 Hz). If the speed of sound is 343 m/s, and the flute is assumed to be a cylinder open at both ends, determine the distance L. f n v n 2L n 1,2,3,4, L 2 nv f n 1 343m s 0.656 m 2 261.6 Hz 17.6 Longitudinal Standing Waves Tube open at one end f n v n 4L n 1,3,5, 34
17.7 Complex Sound Waves 17.7 Complex Sound Waves 35
Assignment pg. 529-531 #19,20,24,28,31,38,43,48 36