Sound Extra Practice: C14.1, 14.1, 14.3, 14.5, 14.9, 14.11, 14.13, 14.15, 14.17, 14.19
Reminders! WebAssign: Better your grade by requesting manual extensions on old assignments (50% recovery). Last homework: Due tomorrow night! Final: May 4, 8-11pm Study by fixing old homeworks, practicing old tests, doing practice test!
Peer Pressure Extra Credits Student evaluations Fill out online If 60% of class fills it out EVERYONE gets +1% on their class grade. Class this Wednesday If 80% of the class participates EVERYONE gets +1% on their class grade. FCI will also be good review for final.
I will email you when I know where the final is. (They haven t told me yet! Sorry!)
Last time (λ) (λ) v = λf = F µ string tension mass density
Important things today Sound as a wave How does it work? Calculating the speed of sound in gasses, liquids, and solids. Quantifying loudness. How loud is 11?
What makes sound? Pitch: determined by wavelength or frequency of vibration. High pitch: high frequency. v = λf This sounds like a silly question but I m asking it to make you think about how that sound is produced, and how it gets to your ears. Every single thing that makes sound is making some kind of vibration. The pitch of that sound is determined by its frequency of vibration. A sound-maker is a vibrating object. And that vibration causes changes in the molecules around them that propagate outward. NOTE here s a tuning fork. It makes sound by vibrating at a fixed frequency.
Thinking about sound Pitch: determined by wavelength or frequency of vibration. High pitch: high frequency (short wavelength). Middle G: f = 392 Hz Pitch (vibration frequency) v = λf Tuning forks work by vibrating, a little bit like a guitar string. I have two tuning forks here. If you put it in water you can see that it s vibrating (it splashes water around!)
Thinking about sound Pitch: determined by wavelength or frequency of vibration. High pitch: high frequency (short wavelength). Which fork will make the higher pitch (assuming they re made from the same material)? A. Longer fork B. Shorter fork C. Both will make the same pitch D. Not enough info Q123 Pitch (vibration frequency) v = λf ANSWER: B. The shorter tuning fork will, generally, have a higher pitch if the two forks are made of the same thickness and material!
What this means Sound moves via compression of molecules! Compression Rarefaction Compression Rarefaction
Note: propagation speed of sound is independent of wave properties! Speed depends ONLY upon the material sound is in. You say but v = λf?!? Raise pitch f, and wavelength λ will decrease! Important to realize: HOW FAST sound moves doesn t depend on the wave itself. It depends ONLY ON THE MATERIAL THE SOUND IS MOVING THROUGH. What can be confusing is this equation - the wavelength and frequency are related! http://www.physicsclassroom.com/mmedia/waves/gsl.cfm
Density of air: 1 kg/m 3 Density of outer space: 0.0000000000000000000000000001 kg/m 3 Why is this a great tagline or even a real physical thing? It s because there are so few molecules in space that sound has trouble propagating. A density wave relies on having molecules to compress. Sound is pretty much lost as soon as it hits the vacuum of space. Another film faux pax, by the way! Come on star wars!
Speed of Sound in a Solid The speed of sound in a solid depends on the material s compressibility and density v = Y ρ Remember last time: wave on a string! v = F µ Y is the Young s Modulus of the material ρ is the density of the material TensileStress = F A = Y ΔL L o Relate to string: tension (how compressible it is) over mass density! YOUNG S MODULUS SHOULD LOOK FAMILIAR!
Ydirt ~ 4x10 7 Pa Ysteel ~ 2x10 11 Pa ρdirt ~ 1250 kg/m 3 ρsteel ~ 8050 kg/m 3 Don t do this for safety s sake! A train turns on < mile away and heads down the line toward you. Will you hear the train first with your ear to the steel tracks, or to the ground (made of loose dirt)? Q124 A. Ground B. Tracks C. Not enough info v = Y ρ Steel is stiffer > higher Y. Steel is denser > higher rho. Dirt: v = 178.9 m/s Steel: v = 4984 m/s ANSWER: B
Speed of Sound in a Liquid In a liquid, the speed also depends on the liquid s compressibility and density v = B ρ Volume Stress = B ΔV V o B is the Bulk Modulus of the liquid ρ is the density of the liquid BUT REMEMBER!!! Temperature affects the volume and density of materials.
Speed of Sound in Air For Earth s atmosphere, the speed of sound is 331 m/s at 0 o C (273 K) Note: for all the materials so far, sound speed goes as 1/sqrt(density)! As the temperature increases, the speed of sound in air A. increases. B. decreases. C. stays the same. If you don t know, you can think about what should happen to a typical material that s heated. Q125 WHAT HAPPENS IF YOU HEAT UP THE AIR? I want you to think and guess: what happens to the sound speed? ANSWER: A.
Speed of Sound in Air For Earth s atmosphere, the speed of sound is 331 m/s at 0 o C (273 K) v = 331m / s T 273K T is in Kelvin!! Speed of sound ~343m/s at room temperature (293 K ~ 20 o C) This equation is calibrated to Earth s atmosphere. I ve swept under the rug some factors of molecular density.
v = 331m / s T 273K A man shouts and hears his echo off a mountain 5 seconds later. How far away is the mountain? Speed of sound in air at room temperature ~343m/s. 343m/s times 2.5 seconds is about 0.5 miles (1mile=1.6 km) [see lightboard notes]
How loud is loud?
The Intensity of Sound Sound energy moves outward in all directions Energy spread over a bigger and bigger sphere! Surface area of sphere = 4 π r 2 I = power area = P 4πr 2 Units of power: Watts (W) Units of intensity: W/m 2 Sound propagates in all directions, and it gets weaker as you move away. We measure the POWER of sound transferred from the source (so how much power is it producing) and we divid that by the AREA OVER WHICH IT S SPREAD AT OUR DISTANCE R. Power is in Watts. Intensity is in W/m2 although we also measure this in decibels, which I ll speak about shortly.
The Intensity of Sound Sound energy moves outward in all directions Energy spread over a bigger and bigger sphere! Surface area of sphere = 4 π r 2 If you get 2x as far, you ll hear a sound with 4x less intensity! I power = area P = 4πr Units of power: Watts (W) Units of intensity: W/m 2 2 Sound propagates in all directions, and it gets weaker as you move away. We measure the POWER of sound transferred from the source (so how much power is it producing) and we divid that by the AREA OVER WHICH IT S SPREAD AT OUR DISTANCE R. Power is in Watts. Intensity is in W/m2 although we also measure this in decibels, which I ll speak about shortly.
Quietest sounds we can hear: 10-12 W/m 2 Sounds that hurt: 1 W/m 2 Difference of 10 12! This is huge! So why don t loud sounds sound 10^12 louder than the quietest sounds?
Alternate Measurement of Intensity Decibels (db) β = 10 log(i/i0) I0 = 10-12 W/m 2 How many times 10 louder is this sound than the faintest hearable sound? Our ears hear in a non-linear way; decibels are a better way to describe this. You can see it as simply a different scaling of Intensity.
ARGH! 10 0 W/m 2 10-2 W/m 2 10-4 W/m 2 10-6 W/m 2 10-8 W/m 2 10-10 W/m 2 10-12 W/m 2 Intensity (W/m 2 ) What u say? Here are intensity using both scales compared with levels of hearing over freq range of hearing. You will have a problem on your homework to practice the use of decibels!
Jet takeoff (25m away): 150 db ARGH! 10 0 W/m 2 10-2 W/m 2 Typical rock concert: 115 db 10-4 W/m 2 10-6 W/m 2 10-8 W/m 2 Intensity (W/m 2 ) Restaurant: 60 db Quiet suburb: 50 db 10-10 W/m 2 10-12 W/m 2 Breathing: 10 db What u say? You will have a problem on your homework to practice this but you shouldn t need to know it for the test.
The rods on the xylophone below generate different frequencies. Why? A) The rods have different densities B) The velocity of sound changes through the rods of differing length. C) The wavelengths vary. D) More than one of the above. Q126 v = Y ρ = λf Same material used Answer: C. Speed of wave depends only on the type of material; the wavelength and frequency are related to keep the velocity the same in a single material!
The Frequency of Sound Audible waves Lay within the normal range of hearing of the human ear Normally between 20 Hz to 20,000 Hz Infrasonic waves Frequencies are below the audible range Earthquakes are an example Ultrasonic waves Frequencies are above the audible range Dog whistles are an example Which one of these do we use for medical purposes? Why?
Applications of Ultrasound High frequency means small wavelength, thus can be used to produce images of small objects v = λf Widely used as a diagnostic and treatment tool Ultrasounds to observe babies in the womb Ultrasonic flow meter to measure blood flow Cavitron Ultrasonic Surgical Aspirator (CUSA) used to surgically remove brain tumors