Lecture 18. Waves and Sound

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1 Lecture 18 Waves and Sound

2 Today s Topics: Nature o Waves Periodic Waves Wave Speed The Nature o Sound Speed o Sound Sound ntensity The Doppler Eect

3 Disturbance Wave Motion DEMO: Rope A wave is a traveling disturbance. A wave carries energy rom place to place.

4 Types o Waves Longitudinal The displacement and propagation directions are collinear Transverse The displacement and propagation directions are perpendicular Waves can be combinations o these two as well!

Periodic Waves Periodic waves consist o cycles or patterns that are produced over and over again by the source Similar to Simple Harmonic Motion Displacement Displacement The amplitude A is the

5 Periodic Waves Periodic waves consist o cycles or patterns that are produced over and over again by the source Similar to Simple Harmonic Motion Displacement Displacement The amplitude A is the maximum excursion o a particle o the medium rom the particles undisturbed position. The wavelength is the horizontal length o one cycle o the wave. The period is the time required or one complete cycle. The requency is related to the period and has units o Hz, or 1/s. 1 T

6 l v T l

7 ACT: out to sea A boat is moored in a ixed location, and waves make it move up and down. the spacing between wave crests is 0 m and the speed o the waves is 5 m/s, how long does it take the boat to go rom the top o a crest to the bottom o a trough? a) 1 second b) seconds c) 4 seconds d) 8 seconds e) 16 seconds We know that v l / T, hence T l / v. l 0 m and v 5 m/s, then T 4 secs. The time to go rom a crest to a trough is only T/ (hal a period), so it takes secs!! t t + Dt

8 ACT: lunch time Microwaves travel with the speed o light, c 3 x 10 8 m/s. At a requency o 10 GHz these waves cause the water molecules in your burrito to vibrate. What is their wavelength? 1 GHz 1 Gigahertz 10 9 cycles/sec a) 0.3 mm b) 3 cm c) 30 cm d) 300 m e) 3 km We know v wave λ T λ H so λ v ( m/s) ( Hz) 3 10 m 3 cm O H

Waves on a string: The speed at which the wave moves to the right depends on

9 What determines v? n general, the wave velocity depends upon the properties o the medium 1. Waves on a string: The speed at which the wave moves to the right depends on how quickly one particle o the string is accelerated upward in response to the net pulling orce. DEMO: wave machine v F m L tension linear density

10 Consider a guitar string v F m L v λ Guitar strings vary in thickness We can also tighten the string, increasing the tension F (tuning)

11 ACT: wave speed A wave pulse can be sent down a rope by jerking sharply on the ree end. the tension o the rope is increased, how will that aect the speed o the wave? a) speed increases b) speed does not change c) speed decreases The wave speed depends on the square root o the tension, so i the tension increases, then the wave speed will also increase.

12 Longitudinal waves and sound The distance between adjacent condensations is equal to the wavelength o the sound wave. Sound travels through gases, liquids, and solids at considerably dierent speeds. DEMO: Bell

13 Pitch and Loudness The requency is the number o cycles per second. A sound with a single requency is called a pure tone. The brain interprets the requency in terms o the subjective quality called pitch. Loudness depends on the amplitude o the pressure wave

14 Sound ntensity Sound waves carry energy that can be used to do work. The amount o energy transported per second is called the power o the wave. The sound intensity is deined as the power that passes perpendicularly through a surace divided by the area o that surace. P A

15 power o sound source P 4p r surace area o sphere

16 ACT: sound intensity You stand a certain distance away rom a speaker and you hear a certain intensity o sound. you double your distance rom the speaker, what happens to the sound intensity at your new position? a) drops to ½ its original value b) drops to ¼ its original value c) drops to 1 / 8 its original value d) drops to 1 / 16 its original value e) does not change at all For a source o a given power P, the intensity is given by P/(4πr ). So i the distance doubles, the intensity must decrease to one-quarter its original value. Follow-up: What distance would reduce the intensity by a actor o 100?

17 Example The intensity o a spherical wave 4.0 m rom the source is 10 W/m. What is the intensity at a point 9.0 m away rom the source? (a)11 W/m (b)4 W/m (c)53 W/m (d)80 W/m (e)70 W/m P 4pr r1 r 1 So, (4.0 m) (9.0 m) 10 W/m W/m

logarithmic scale called the intensity level: β ( 10 db)log o o 1.

18 ntensity and Hearing The decibel (db) is a measurement unit used when comparing two sound intensities. Because o the way in which the human hearing mechanism responds to intensity, it is appropriate to use a logarithmic scale called the intensity level: β ( 10 db)log o o W m The threshold o hearing Note that log(1) 0, so when the intensity o the sound is equal to the threshold o hearing, the intensity level is zero.

19 The db scale is logarithmic A person was talking in a small room; and the sound intensity level is 60 db everywhere within the room. Now, there are eight people talking in similar manner simultaneously in the room, what is the sound intensity level? (a) 61 db (b)79 db (c) 480 db (d) 64 db (e) 69 db ( ) db db db db db db 9 8 )log (10 )log (10 log log ) (10 )log (10 )log ( ø ö è æ - ú û ù ê ë é ø ö è æ - ø ö è æ - ø ö è æ ø ö è æ Let b b b b b b

20 ACT: decibel level A quiet radio has an intensity level o about 40 db. Busy street traic has a level o about 70 db. How much greater is the intensity o the street traic compared to the radio? a) about the same b) about 10 times c) about 100 times d) about 1000 times e) about 10,000 times increase by 10 db increase intensity by actor o 10 1 (10) increase by 0 db increase intensity by actor o 10 (100) increase by 30 db increase intensity by actor o 10 3 (1000)

The Doppler Eect The Doppler eect is the change in requency or pitch o the sound detected by an observer because the sound source and the observer have dierent velocities with respect to the medium o

21 The Doppler Eect The Doppler eect is the change in requency or pitch o the sound detected by an observer because the sound source and the observer have dierent velocities with respect to the medium o sound propagation. For a moving source: o l l! v s T v v l l! v T s v s v! v s s DEMO: Whistle o s æ 1 è1! v s ö v ø (-) means source moving towards observer (+) means source moving away rom observer

For a stationary source and moving observer: Both the source and observer moving: Numerator: plus sign applies when observer moves towards the source o o s s v ± o l æ 1 ± è v v o ö ø s æ 1 ± è

22 For a stationary source and moving observer: Both the source and observer moving: Numerator: plus sign applies when observer moves towards the source o o s s v ± o l æ 1 ± è v v o ö ø s æ 1 ± è v ö o sl ø (+) means observer moving towards source (-) means observer moving away rom source o s æ v ± o 1 v vs 1! è v ö ø Denominator: minus sign applies when source moves towards the observer

23 ACT: Doppler eect Observers A, B, and C listen to a moving source o sound. The location o the wave ronts o the moving source with respect to the observers is shown below. Which o the ollowing is true? a) requency is highest at A b) requency is highest at B c) requency is highest at C d) requency is the same at all three points The number o wave ronts hitting observer C per unit time is greatest thus the observed requency is highest there. Follow-up: Where is the requency lowest?

Thermodynamics continued

Chapter 15 Thermodynamics continued 15 Work The area under a pressure-volume graph is the work for any kind of process. B Pressure A W AB W AB is positive here volume increases Volume Clicker Question