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Waves and Sound. You may not realize it, but you are surrounded by waves. The “waviness” of a water wave is readily apparent. Sound and light are also waves with many of the same properties. Chapter Goal: To learn the basic properties of waves, using sound waves as the example.
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Waves and Sound You may not realize it, but you are surrounded by waves. The “waviness” of a water wave is readily apparent. Sound and light are also waves with many of the same properties. Chapter Goal: To learn the basic properties of waves, using sound waves as the example.
16.1 The Nature of Waves • A wave is a traveling disturbance. • A wave carries energy from place to place. • Most waves travel through a medium, such as air, water, wire, or a Slinky. • Electromagnetic waves (including light) do not need a medium to propagate, and can travel in a vacuum.
Longitudinal Waves Transverse Waves
16.2 Periodic Waves Periodic waves consist of cycles or patterns that are produced over and over again by the source. In the figures, every segment of the slinky vibrates in simple harmonic motion, provided the end of the slinky is moved in simple harmonic motion. Transverse Longitudinal
“snapshot” “history” • The amplitude (A) maximum change of a particle of the medium from equilibrium value (may not be zero!). The SI units of amplitude depend on the wave. • The wavelength λis the horizontal length of one cycle of the wave. SI units are meters. • The period T is the time required for one complete cycle. SI units are seconds. • In the drawing, one cycleis shaded in color. • The left-hand graph shows amplitude vs. displacement. • The right-hand graph shows amplitude vs. time.
16.2 Periodic Waves In the drawing, one cycleis shaded in color. • The frequency f is the number or waves (or cycles) that pass by in a given time. The units are cycles per second, called Hertz (Hz), or s-1 • Frequency is the reciprocal of period. • The speed (v) of a wave in m/s can be determined by dividing the wavelength, λ, by the period, T:
What is the frequency? • .1 Hz • .2 Hz • 2 Hz • 5 Hz • 10 Hz
2 Waves The graphs below show amplitude as a function of position (a “snapshot” graph). Both waves travel at the same speed through the same medium. Which wave has the greater frequency? A. I B. II C. Both have same frequency D. Can’t tell from graph
Speed of a wave on a string The speed at which the wave moves to the right depends on how quickly one particle of the string is accelerated upward in response to the net pulling force. tension in the string linear density (mass per unit length of string
How long is the string? The mass of a string is 8.00 x10-3 kg, and it is stretched so the tension in it is 220 N. A transverse wave traveling on this string has a frequency of 260 Hz and a wavelength of 0.60 m. What is the length of the string?
How long is the string The mass of a string is 8.00 x10-3 kg, and it is stretched so the tension in it is 220 N. A transverse wave traveling on this string has a frequency of 260 Hz and a wavelength of 0.60 m. What is the length of the string? Ans: 0.885m
LONGITUDINAL SOUND WAVES • Sound travels in a longitudinal wave, like a slinky. • The medium can be gas, liquid or solid. We will investigate sound waves traveling in a gas. • Condensation refers to when the air molecules are compressed • Rarefaction refers to when the air molecules are “stretched” apart.
16.5 Wavelength and Frequency • Wavelength: the distance between adjacent condensations (or rarefactions). SI units are meters • Frequency: the number of cycles per second that passes by a given location. Each cycle includes one condensation and one rarefaction. • Pitch (piccolo vs tuba) is an attribute of sound influenced by its frequency
Amplitude vs. Distance Graph • The amplitude of a sound wave is expressed in units of pressure (N/m2 ). Condensations are the peaks, with higher-than-atmospheric pressure, rarefactions are the troughs, with lower pressure. • Note the tube shows the sound wave is a longitudinal wave, even though its graph looks like a transverse wave • Loudness is an attribute of sound that depends primarily on the pressure amplitude of the sound wave.
16.5 Speed of Sound Waves • Waves transfer energy, not matter. • Energy is transferred when individual, vibrating air molecules collide with their neighbors, moving the rarefactions and condensations in the direction of wave travel.
The speed of molecules undergoing collisions in an ideal gas such as air is found using principles of Kinetic Theory of gases. • Experiments shows that the speed of air in an ideal gas is: • What do all the variables mean?
T - the temperature in Kelvin (Tc + 273) • k - Boltzmann’s constant, • γ (gamma) - ratio of specific heat capacities at constant pressure to that of constant volume Cp/Cv Don’t confuse γ with λ, the constant for wavelength! • γ = 1. 4 (7/5) for air and other diatomic gases. • γ = 1.67 (5/3) for a monatomic gas • m - the mass of a molecule of the gas in kg, a very small number!
16.6 The Speed of Sound Sound waves travel through gases, liquids, and solids at considerably different speeds.
The ultrasonic ruler An ultrasonic ruler sends out a sound wave which travels to the wall and back. The round trip travel time is 20.0 ms and the air temperature is 32° C. The average molecular mass of air is 28.9 u. What is the distance to the wall?
The ultrasonic ruler An ultrasonic ruler sends out a sound wave which travels to the wall and back. The round trip travel time is 20.0 ms and the air temperature is 32° C. The average molecular mass of air is 28.9 u. What is the distance to the wall? Ans: 3.5 m
Speed of sound Carbon monoxide (CO), Hydrogen gas (H2) and nitrogen (N2) are all diatomic gases that behave as ideal. In which gas does sound travel the fastest at a given temperature? A. CO B. H2 C. N2
16.9 The Doppler Effect The Doppler effect is the change in frequency or pitch of the sound detected by an observer because the sound source and the observer have different velocities with respect to the medium of sound propagation.
Doppler Effect Video Pitch is related to the frequency that you hear. As you listen, pay attention to what happens to the pitch, as opposed to the loudness, of the sound http://www.youtube.com/watch?v=a3RfULw7aAY&feature=related http://www.youtube.com/watch?v=_UXtort76gY 3:30seconds
Dopper Effect Simulation http://www.walter-fendt.de/ph14e/dopplereff.htm http://www.youtube.com/watch?v=4mUjM1qMaa8&feature=fvwrel
Source moving toward stationary observer Wavelength perceived by stationary observer is smaller than that perceived by moving source. o – observer s – source v without subscript is the speed of sound in air at 20° C (343m/s) unless otherwise noted Frequency perceived by stationary observer is larger than that perceived by the moving source.
Source moving toward or away from stationary observer If the source moves towards the observer If the source moves away, note the frequency heard by the observer will now be less than that that perceived by the source
The Opera Singer An opera singer in a convertible sings a note at 600 Hz while cruising down the highway at 25 m/s. What is the frequency heard by: • a person standing on the sidewalk in front of the car • a person standing on the sidewalk behind the car.
The Opera Singer An opera singer in a convertible sings a note at 600 Hz while cruising down the highway at 25 m/s. What is the frequency heard by: • a person standing on the sidewalk in front of the car: 650 (647) Hz • a person standing on the sidewalk behind the car: 560 (559) Hz
Moving observer, stationary source Observer moving towards stationary source will perceive a higher frequency than that perceived by the source Observer moving away from stationary source
16.9 The Doppler Effect GENERAL CASE – When both source and observer are moving toward/away from/ each other Numerator: plus sign applies when observer moves towards the source Denominator: minus sign applies when source moves towards the observer
The Opera Singer Revisited An opera singer sings a note at 600 Hz in a large outdoor amphitheater. What is the frequency heard by: • a person driving towards her at 25 m/s? • a person driving away from her at 25 m/s.
The Opera Singer Revisited An opera singer sings a note at 600 Hz in a large outdoor amphitheater. What is the frequency heard by: • a person driving towards her at 25 m/s? 644 m/s • a person driving away from her at 25 m/s? – 556 m/s
Amy and Zach are both listening to a source of sound waves moving to the right. What frequency does Zach hear relative to the source? a. higher b. lower c. the same Amy Zach
Amy and Zach are both listening to a source of sound waves moving to the right. What frequency does Amy hear, relative to the source? a. higher b. lower c. the same Amy Zach
A B C D
Doppler shift question A red car and a blue car can move along the same straight one-lane road. Both cars can move only at one speed when they move (e.g., 60 mph). The driver of the red car sounds his horn. In which one of the following situations does the driver of the blue car hear the highest horn frequency? • Both cars move apart • Both cars move in the same direction • Both cars move toward each other • Red car moves toward stationary blue car • Blue car moves toward stationary red car.
Doppler shift question A red car and a blue car can move along the same straight one-lane road. Both cars can move only at one speed when they move (e.g., 60 mph). The driver of the red car sounds his horn. In which one of the following situations does the driver of the blue car hear the highest horn frequency? • Both cars move apart • Both cars move in the same direction • Both cars move toward each other • Red car moves toward stationary blue car • Blue car moves toward stationary red car.
16.7 Sound Intensity • Sound waves transfer energy • The amount of energy transported per second (Joules per second) is called the power of the wave. • The sound intensity is defined as the power to area ratio. It is related to (but not the same as!) the loudness of the sound. • The energy released by the source, and therefore the power, are the same, regardless of the distance of the listener. • The sound intensity is proportional to the inverse square of the distance
Physical Therapy Deep ultrasonic heating is used to promote healing of torn tendons (and foot massage?). It is produced by applying ultrasonic sound over the affected area of the body. The sound transducer (generator) is circular with a radius of 1.8 cm, and it produces a sound intensity of 5.9 x 103 W/m2. How much time is required for the transducer to emit 3900 J of sound energy?
Physical Therapy Deep ultrasonic heating is used to promote healing of torn tendons (and foot massage?). It is produced by applying ultrasonic sound over the affected area of the body. The sound transducer (generator) is circular with a radius of 1.8 cm, and it produces a sound intensity of 5.9 x 103 W/m2. How much time is required for the transducer to emit 3900 J of sound energy? Ans: 649s (my turn next, please!)
If the source emits sound uniformly in all directions, the intensity depends on the distance from the source in a simple way. Model the area around the sound source as a sphere The sound intensity is the ratio of power to the surface area of the sphere. Don’t confuse that with the area of a circle, or the volume of a sphere! Surface area of sphere
Was it as good for you? Assume that the sound spreads out uniformly and any ground reflections can be ignored. Listener 2 is twice as far from the explosion as Listener 1. If L1 hears with an intensity of 1 W/m2, with what intensity does L 2 hear? a. 2 b. ½ c. 4 d. ¼
Fireworks I2/I1 = (P/4πr22) = r1 2/r2 2 , = r2/4r2 (P/4πr12) a. 2 b. ½ c. 4 d. ¼
Decibels – a measure of loudness • Human hearing spans an extremely wide range of intensities • threshold of hearing at ≈ 1 × 10−12 W/m2 • threshold of pain at ≈ 10 W/m2. • To cover a large range, scientists use a logarithmic scale. Sorry about that. • It is logical to place the “zero” of this scale at the threshold of hearing, so I0 = 1 × 10−12 W/m2 • We define the sound intensity level, expressed in decibels (dB), as: Tests show that 1dB is approximately the minimum change in loudness the average human can detect.
16.8 Decibels Example 9 Comparing Sound Intensities Audio system 1 produces a sound intensity level of 90.0 dB, and system 2 produces an intensity level of 93.0 dB. Determine the ratio of intensities.
16.8 Decibels β1 = 93 dB, β2 = 90 dB, Find I2/I1 Recall that subtracting log quantities is equivalent to taking the log of their ratio. Divide both sides by 10 dB Take the antilog of both sides (10x function on most calculators) Although I2 is twice that of I1, the sound is not twice as loud. Experimental data show that it takes a 10 dB difference for a sound to be perceived as “twice as loud”. This corresponds to an order of magnitude difference in intensities.
