Chapter 16. Waves and Sound

Transcription

1 Chapter 16 Waes and Sound

2 16.1 The Nature of Waes 1. A wae is a traeling disturbance. 2. A wae carries energy from place to place.

3 16.1 The Nature of Waes Transerse Wae

4 16.1 The Nature of Waes Longitudinal Wae

5 16.1 The Nature of Waes Water waes are partially transerse and partially longitudinal.

6 16.2 Periodic Waes Periodic waes consist of cycles or patterns that are produced oer and oer again by the source. In the figures, eery segment of the slinky ibrates in simple harmonic motion, proided the end of the slinky is moed in simple harmonic motion.

7 16.2 Periodic Waes 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 waelength is the horizontal length of one cycle of the wae. The period is the time required for one complete cycle. The frequency is related to the period and has units of Hz, or s -1. f 1 T

8 16.2 Periodic Waes λ T fλ

9 16.2 Periodic Waes Example 1 The Waelengths of Radio Waes AM and FM radio waes are transerse waes consisting of electric and magnetic field disturbances traeling at a speed of 3.00x10 8 m/s. A station broadcasts AM radio waes whose frequency is 1230x10 3 Hz and an FM radio wae whose frequency is 91.9x10 6 Hz. Find the distance between adjacent crests in each wae. λ T fλ λ f

10 16.2 Periodic Waes AM f λ m s Hz 244 m FM f λ m s Hz 3.26 m

11 16.3 The Speed of a Wae on a String The speed at which the wae moes to the right depends on how quickly one particle of the string is accelerated upward in response to the net pulling force. F m L tension linear density

12 16.3 The Speed of a Wae on a String Example 2 Waes Traeling on Guitar Strings Transerse waes trael on each string of an electric guitar after the string is plucked. The length of each string between its two fixed ends is m, and the mass is 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 waes on the two strings.

13 16.3 The Speed of a Wae on a String High E F m L 226 N 3 ( kg) ( m) - 826m s Low E F m L 226 N 3 ( kg) ( m) m s

14 16.3 The Speed of a Wae on a String Conceptual Example 3 Wae Speed Versus Particle Speed Is the speed of a transerse wae on a string the same as the speed at which a particle on the string moes?

15 16.4 The Mathematical Description of a Wae What is the displacement y at time t of a particle located at x?

16 16.5 The Nature of Sound Waes LONGITUDINAL SOUND WAVES

17 16.5 The Nature of Sound Waes The distance between adjacent condensations is equal to the waelength of the sound wae.

18 16.5 The Nature of Sound Waes Indiidual air molecules are not carried along with the wae.

19 16.5 The Nature of Sound Waes 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 subjectie quality called pitch.

20 16.5 The Nature of Sound Waes THE PRESSURE AMPLITUDE OF A SOUND WAVE Loudness is an attribute of a sound that depends primarily on the pressure amplitude of the wae.

21 16.6 The Speed of Sound Sound traels through gases, liquids, and solids at considerably different speeds.

22 16.6 The Speed of Sound In a gas, it is only when molecules collide that the condensations and rarefactions of a sound wae can moe from place to place. 3kT rms m Ideal Gas γ kt m k J K γ 5 3 or 7 5

23 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. Diide the number of seconds by fie. The result gies the approximate distance (in miles) to the thunderstorm. Why does this rule work?

24 16.6 The Speed of Sound LIQUIDS SOLID BARS B ad ρ Y ρ

25 16.7 Sound Intensity Sound waes carry energy that can be used to do work. The amount of energy transported per second is called the power of the wae. The sound intensity is defined as the power that passes perpendicularly through a surface diided by the area of that surface. I P A

26 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.

27 16.7 Sound Intensity I W W m m A P I W W m m A P

28 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.

29 16.7 Sound Intensity power of sound source I P 4π r 2 area of sphere

30 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, oerestimate, or gie the correct sound intensity? I P 4π r 2

31 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 leel: β I ( 10 db) log I o I o W m 2 Note that log(1)0, so when the intensity of the sound is equal to the threshold of hearing, the intensity leel is zero.

32 16.8 Decibels β ( 10 db) log I o I I o W m 2

33 16.8 Decibels Example 9 Comparing Sound Intensities Audio system 1 produces a sound intensity leel of 90.0 db, and system 2 produces an intensity leel of 93.0 db. Determine the ratio of intensities. β ( 10 db) log I o I

34 16.8 Decibels β I ( 10 db) log I o I 1 β ( ) 1 10 db log β ( ) I o 2 10 db log I o I 2 I I I I I β2 β1 log o 2 ( 10 db) log ( 10 db) log ( 10 db) log ( 10 db) I o Io I1 Io I1 3.0 db I 2 ( 10 db) log I I log I 2 1 I I

35 16.9 The Doppler Effect The Doppler effect is the change in frequency or pitch of the sound detected by an obserer because the sound source and the obserer hae different elocities with respect to the medium of sound propagation.

36 16.9 The Doppler Effect MOVING SOURCE s T λ λ s s s s o f f T f λ λ f f s s o 1 1

37 16.9 The Doppler Effect f f s s o 1 1 source moing toward a stationary obserer source moing away from a stationary obserer + f f s s o 1 1

38 16.9 The Doppler Effect Example 10 The Sound of a Passing Train A high-speed train is traeling 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 waelength of the sound, as perceied by a person standing at the crossing, when the train is (a) approaching and (b) leaing the crossing? f o f s 1 1 s f o f s 1 1+ s

39 16.9 The Doppler Effect approaching f o 1 1 ( 415 Hz) 477 Hz 44.7m s 343m s leaing f o 1+ 1 ( 415 Hz) 367 Hz 44.7m s 343m s

40 16.9 The Doppler Effect MOVING OBSERVER f o f s + o λ f s 1 + o fsλ f s 1 + o

41 16.9 The Doppler Effect Obserer moing towards stationary source f fs + o 1 o Obserer moing away from stationary source f f s o 1 o

42 16.9 The Doppler Effect GENERAL CASE Numerator: plus sign applies when obserer moes towards the source f o f s 1 ± 1 o s Denominator: minus sign applies when source moes towards the obserer

43 16.10 Applications of Sound in Medicine By scanning ultrasonic waes across the body and detecting the echoes from arious locations, it is possible to obtain an image.

44 16.10 Applications of Sound in Medicine Ultrasonic sound waes cause the tip of the probe to ibrate at 23 khz and shatter sections of the tumor that it touches.

45 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 moing.

46 16.11 The Sensitiity of the Human Ear