Physics 101: Lecture 22, Pg 1 Physics 101: Lecture 22 Sound Today’s lecture will cover Textbook Chapter 12 EXAM III

Physics 101: Lecture 22, Pg 2 Speed of Sound Recall for pulse on string: v = sqrt(T /  ) For fluids: v = sqrt(B/  ) MediumSpeed (m/s) Air343 Helium972 Water1500 Steel5600 B = bulk modulus

Physics 101: Lecture 22, Pg 3 Velocity ACT A sound wave having frequency f 0, speed v 0 and wavelength 0, is traveling through air when in encounters a large helium-filled balloon. Inside the balloon the frequency of the wave is f 1, its speed is v 1, and its wavelength is 1 Compare the speed of the sound wave inside and outside the balloon 1. v 1 < v 0 2. v 1 = v 0 3. v 1 > v 0 V 1 =965m/s V 0 =343m/s correct

Physics 101: Lecture 22, Pg 4 Frequency ACT A sound wave having frequency f 0, speed v 0 and wavelength 0, is traveling through air when in encounters a large helium-filled balloon. Inside the balloon the frequency of the wave is f 1, its speed is v 1, and its wavelength is 1 Compare the frequency of the sound wave inside and outside the balloon 1. f 1 < f 0 2. f 1 = f 0 3. f 1 > f 0 f1f1 f0f0 correct Time between wave peaks does not change!

Physics 101: Lecture 22, Pg 5 Wavelength ACT A sound wave having frequency f 0, speed v 0 and wavelength 0, is traveling through air when in encounters a large helium-filled balloon. Inside the balloon the frequency of the wave is f 1, its speed is v 1, and its wavelength is 1 Compare the wavelength of the sound wave inside and outside the balloon 1. 1 < = > correct = v / f

Physics 101: Lecture 22, Pg 6 Intensity and Loudness l Intensity is the power per unit area. è I = P / A è Units: Watts/m 2 l For Sound Waves  I = p 0 2 / (2  v) (p o is the pressure amplitude) è Proportional to p 0 2 (note: Energy goes as A 2 ) l Loudness (Decibels) è Loudness perception is logarithmic è Threshold for hearing I 0 = W/m 2   = (10 dB) log 10 ( I / I 0 )   2 –  1 = (10 dB) log 10 (I 2 /I 1 )

Physics 101: Lecture 22, Pg 7 Log 10 Review l Log 10 (1) = 0 l Log 10 (10) = 1 l Log 10 (100) = 2 l Log 10 (1,000) = 3 l Log 10 (10,000,000,000) = 10

Physics 101: Lecture 22, Pg 8 Decibels ACT l If 1 person can shout with loudness 50 dB. How loud will it be when 100 people shout? 1) 52 dB2) 70 dB3) 150 dB  100 –  1 = (10 dB) log 10 (I 100 /I 1 )  100 = 50 + (10 dB) log 10 (100/1)  100 =

Physics 101: Lecture 22, Pg 9 Amazing Ear (not on exam) l Your Ear is sensitive to an amazing range! 1dB – 100 dB è Watts/m 2 è 1 Watt/m 2 l Like a laptop that can run using all power of è Battery è Entire Nuclear Power Plant

Physics 101: Lecture 22, Pg 10 Intensity ACT l Recall Intensity = P/A. If you are standing 6 meters from a speaker, and you walk towards it until you are 3 meters away, by what factor has the intensity of the sound increased? 1) 22) 43) 8 Area goes as d 2 so if you are ½ the distance the intensity will increase by a factor of 4 Speaker radiating power P I 1 = P/(4  D 1 2 ) D1D1 I 2 = P/(4  D 2 2 ) D2D2

Physics 101: Lecture 22, Pg 11 Standing Waves in Pipes Open at both ends: Pressure Node at end  = 2 L / n n=1,2,3.. Open at one end: Pressure AntiNode at closed end : = 4 L / n n odd I do not understand what a node is (in standing waves).

Physics 101: Lecture 22, Pg 12 Organ Pipe Example A 0.9 m organ pipe (open at both ends) is measured to have its first harmonic at a frequency of 382 Hz. What is the speed of sound in the pipe? Pressure Node at each end. = 2 L / n n=1,2,3.. = L for first harmonic (n=2) f = v / v = f = (382 s -1 ) (0.9 m) = 343 m/s

Physics 101: Lecture 22, Pg 13 Resonance ACT l What happens to the fundamental frequency of a pipe, if the air (v=343 m/s) is replaced by helium (v=972 m/s)? 1) Increases2) Same3) Decreases f = v/

Physics 101: Lecture 22, Pg 14 Preflight 1 l As a police car passes you with its siren on, the frequency of the sound you hear from its siren 1) Increases2) Decreases3) Same Doppler Example Audio Doppler Example Visual Increases as the car approaches and decreases as it moves away...it is the essence of the Doppler Affect My reasoning is from experience.

Physics 101: Lecture 22, Pg 15 Doppler Effect moving source v s l When source is coming toward you (v s > 0) è Distance between waves decreases è Frequency is higher l When source is going away from you (v s < 0) è Distance between waves increases è Frequency is lower l f o = f s / (1- v s /v)

Physics 101: Lecture 22, Pg 16 Doppler Effect moving observer (v o ) l When moving toward source (v o < 0) è Time between waves peaks decreases è Frequency is higher l When away from source (v o > 0) è Time between waves peaks increases è Frequency is lower l f o = f s (1- v o /v) Combine: f o = f s (1-v o /v) / (1-v s /v)

Physics 101: Lecture 22, Pg 17 Doppler ACT A: You are driving along the highway at 65 mph, and behind you a police car, also traveling at 65 mph, has its siren turned on. B: You and the police car have both pulled over to the side of the road, but the siren is still turned on. In which case does the frequency of the siren seem higher to you? A. Case A B. Case B C. same vsvs f vovo f’ v correct

Physics 101: Lecture 22, Pg 18 Doppler sign convention Doppler shift: fo = fs (1-vo/v) / (1-vs/v) vs = v(source) vo = v(observer) v = v(wave) + If same direction as sound wave - If opposite direction to sound wave Vo/Vs negative or positive

Physics 101: Lecture 22, Pg 19 Constructive interference Destructive interference Interference and Superposition

Physics 101: Lecture 22, Pg 20 Superposition & Interference l Consider two harmonic waves A and B meeting at x=0.  Same amplitudes, but  2 = 1.15 x  1. l The displacement versus time for each is shown below: What does C(t) = A(t) + B(t) look like?? A(  1 t) B(  2 t)

Physics 101: Lecture 22, Pg 21 Superposition & Interference l Consider two harmonic waves A and B meeting at x=0.  Same amplitudes, but  2 = 1.15 x  1. l The displacement versus time for each is shown below: A(  1 t) B(  2 t) CONSTRUCTIVE INTERFERENCE DESTRUCTIVE INTERFERENCE C(t) = A(t) + B(t)

Physics 101: Lecture 22, Pg 22 Beats l Can we predict this pattern mathematically? è Of course! l Just add two cosines and remember the identity: whereand cos(  L t)

Physics 101: Lecture 22, Pg 23Summary Speed of sound v = sqrt(B/  ) Intensity  = (10 dB) log 10 ( I / I 0 ) l Standing Waves è f n = n v/(2L) Open at both ends n=1,2,3… è f n = n v/(4L) Open at one end n=1,3,5… l Doppler Effect f o = f s (v-v o ) / (v-v s ) l Beats