Chapter 14 Waves and Sound. Copyright 2010 Pearson Education, Inc.

Transcription

1 Chapter 14 Waes and Sound

2 Units of Chapter 14 Types of Waes Waes on a String Harmonic Wae Functions Sound Waes Sound Intensity The Doppler Effect We will leae out Chs and

3 14-1 Types of Waes A wae is a disturbance that propagates from one place to another. The easiest type of wae to isualize is a transerse wae, where the displacement of the medium is perpendicular to the direction of motion of the wae.

4 14-1 Types of Waes In a longitudinal wae, the displacement is along the direction of wae motion.

5 14-1 Types of Waes Water waes are a combination of transerse and longitudinal waes.

6 14-1 Types of Waes Waelength λ: distance oer which wae repeats Period T: time for one waelength to pass a gien point Frequency f: Speed of a wae:

7 14-2 Waes on a String The speed of a wae is determined by the properties of the material through which it propagates. For a string, the wae speed is determined by: 1. the tension in the string, and 2. the mass of the string. As the tension in the string increases, the speed of waes on the string increases as well.

8 14-2 Waes on a String The total mass of the string depends on how long it is; what makes a difference in the speed is the mass per unit length. We expect that a larger mass per unit length results in a slower wae speed.

9 14-2 Waes on a String As we can see, the speed increases when the force increases, and decreases when the mass increases.

10 Example: When the tension in a cord is 75.0 N, the wae speed is 140 m/s. What is the linear mass density of the cord? The speed of a wae on a string is = F µ Soling for the linear mass density: F µ = 2 = 75.0 N 3 = 3.8" 10 ( 140 m/s) 2 kg/m

11 14-2 Waes on a String When a wae reaches the end of a string, it will be reflected. If the end is fixed, the reflected wae will be inerted:

12 14-2 Waes on a String If the end of the string is free to moe transersely, the wae will be reflected without inersion.

13 14-3 Harmonic Wae Functions Since the wae has the same pattern at x + λ as it does at x, the wae must be of the form Also, as the wae propagates in time, the peak moes as

14 14-3 Harmonic Wae Functions Combining yields the full wae equation:

15 Example: What is the waelength of a wae whose speed and period are 75.0 m/s and 5.00 ms, respectiely? = f = T Soling for the waelength: # = ( )( " m/s s) m T = =

16 Example: A wae on a string has an equation: ( 4.00 mm) sin( 600 rad/sec) t ( 6.00 rad/m) x) y ( x, t) = Compare this to ( t kx) y ( x, t) = Asin " (a) What is the amplitude of the wae? A = 4.00 mm (b) What is the waelength? The wae number k is 6.00 rad/m. " = 2 k = rad/m = 105. m

17 Example continued: (c) What is the period? T # 2# = = = 105. " rad/sec 2 2 sec (d) What is the wae speed? = ) f = & % ) # 2( " ' k 600 rad/sec 6.00 rad/m ( 2( f ) = = = 100 m/s (e) What direction is the wae traeling. Along the +x direction.

18 14-4 Sound Waes Sound waes are longitudinal waes, similar to the waes on a Slinky: Here, the wae is a series of compressions and stretches.

19 14-4 Sound Waes In a sound wae, the density and pressure of the air (or other medium carrying the sound) are the quantities that oscillate.

20 14-4 Sound Waes The speed of sound is different in different materials; in general, the denser the material, the faster sound traels through it.

21 14-4 Sound Waes Sound waes can hae any frequency; the human ear can hear sounds between about 20 Hz and 20,000 Hz. Sounds with frequencies greater than 20,000 Hz are called ultrasonic; sounds with frequencies less than 20 Hz are called infrasonic. Ultrasonic waes are familiar from medical applications; elephants and whales communicate, in part, by infrasonic waes.

22 14-6 The Doppler Effect The Doppler effect is the change in pitch of a sound when the source and obserer are moing with respect to each other. When an obserer moes toward a source, the wae speed appears to be higher, and the frequency appears to be higher as well.

23 14-6 The Doppler Effect The new frequency is: If the obserer were moing away from the source, only the sign of the obserer s speed would change:

24 To summarize: 14-6 The Doppler Effect

25 14-6 The Doppler Effect The Doppler effect from a moing source can be analyzed similarly; now it is the waelength that appears to change:

26 14-6 The Doppler Effect We find:

27 14-6 The Doppler Effect Combining results gies us the case where both obserer and source are moing: The Doppler effect has many practical applications: weather radar, speed radar, medical diagnostics, astronomical measurements.

28 Example: A source of sound waes of frequency 1.0 khz is stationary. An obserer is traeling at 0.5 times the speed of sound. (a) What is the obsered frequency if the obserer moes toward the source? 1.5 khz = = " # % & ' ' ' = " # % & ' ' = f f f f s s s o o f o is unknown; f s = 1.0 khz; o = 0.5; s = 0; and is the speed of sound.

29 (b) Repeat, but with the obserer moing in the other direction. 0.5 khz = = " # % & ' + ' = " # % & ' ' = f f f f s s s o o f o is unknown; f s = 1.0 khz; o = +0.5; s = 0; and is the speed of sound. Example continued: