Nature of Sound Wave Sound is a mechanical, longitudinal, pressure wave.
Nature of Sound Wave What, exactly, is oscillating? Air molecules are compressed together by the mechanical motion of some solid matter. The compressions and rarefactions propagate through the medium
Terminology Compressions are areas of increased molecular density Rarefactions are regions of decreased density
Speed of Sound 05 MediumSpeed (m/s) Air343 Helium972 Water1500 Steel5600 Recall that the bulk modulus is the ratio of the stress to the strain. It is an effective “spring constant” for the fluid
TnR How would you expect the speed of sound in air (v) to depend on the temperature (T) of the air? 1. v will increase as T increases 2. v will decrease as T increases 3. v will not depend on T
Temperature Dependence As the air heats up, the molecules move faster and the pressure wave passes through the medium faster. The functional relationship is given by the empirical formula:
Paint Bomb Suppose a paint bomb exploded. How would the thickness of the paint on your face depend on how far you were from the bomb?
Energy and Intensity Waves transmit energy The rate that energy is transmitted is the power. What is intensity? Intensity is the “concentration” of power on a particular area Intensity is the rate at which energy flows to a given area, perpendicular to the direction of wave travel.
Example of Spherical Waves Assume that a 100 W speaker radiates energy outwards in a sphere. What is the intensity of this sound a distance of 3 meters from the source.
Intensity TnR 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? A: 2 B: 4 C: 8 D: ½ E: ¼ 27
Graph This Data: SourceIntensity Gentle Breeze1E-11 W/m 2 Whisper5E-9 W/m 2 Conversation2E-6 W/m 2 Orchestra6E-3 W/m 2 iPod on Max w/ earbuds0.02 W/m 2 F-16 at Takeoff100 W/m 2
Your Ear Your Ear is sensitive to an amazing range! (1dB – 100 dB) Lowest limit: 10 -12 Watts/m 2 Upper limit: 1 Watt/m 2 Like a laptop that can run using all power of A single battery Entire Nuclear Power Plant 23
The Ear We (humans) do not have a linear response to sound. When the intensity doubles, we do not register that the sound is twice as loud. Our response is actually more logarithmic It makes sense then to define an intensity scale that is more matched to what we experience
Intensity Scale Intensity scale is a log scale, called the decibel scale. It measures the intensity relative to a reference level, known as the threshold of hearing. I o = 1 x 10 -12 W/m 2.
Examples A speaker emits 600 Joules of energy each second. Assuming a spherical wave, calculate the intensity (in decibels) a distance of 5 meters away from the source. = 122.8 dB Find the power of a source if the intensity at a distance of 120 meters is 65 dB.
Example Problem #1 A sound wave has an intensity of 0.0533 W/m2. What is the intensity of this sound in db? A pair of headphones reduce the noice level by 25db. What intensity would reach your ears if you were wearing these headphones?
Example Problem #2 A loud, obnoxious student at a swim meet (let’s call him Ryan*) can produce a sound level of 90 db at a distance of 2 meters. Find the intensity of this wave. What power is required to produce this wave, assuming that it is spherically distributed. *Note: this is a hypothetical student and any resemblance to any actual student you may or may not know is purely coincidental.
TnR 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 36
Doppler Effect, moving source When source is coming toward you (v s > 0) Distance between waves decreases Frequency increases When source is going away from you (v s < 0) Distance between waves increases Frequency decreases 38
Doppler Effect, moving observer When moving toward source (v o < 0) Time between waves peaks decreases Frequency increases When away from source (v o > 0) Time between waves peaks increases Frequency decreases 40
Doppler TnR 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? 1. Case A 2. Case B 3. same correct 44
Sonic Boom When the velocity is greater than the speed of sound, the pressure waves build up along a cone that trails the source. Mach = velocity of source / velocity of sound Visualizations: http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=21 http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=21