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Following key concepts are discussed in these Lecture Slides : Physics, Velocity, Quantities, Units, Vectors, Displacement, Graphing Motion, Kinematics, Vectors, Weight
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Longitudinal Waves
Pressure Graphs
Speed of Sound
Wavefronts
Frequency & Pitch (human range)
The Human Ear
Sonar & Echolocation
Doppler Effect (and sonic booms)
Interference Standing Waves in a String: Two fixed ends Standing Waves in a Tube: One open end Two open ends Musical Instruments (and other complex sounds) Beats Intensity Sound Level (decibels)
As you learned in the unit on waves, in a longitudinal wave the particles in a medium travel back & forth parallel to the wave itself. Sound waves are longitudinal and they can travel through most any medium, so molecules of air (or water, etc.) move back & forth in the direction of the wave creating high pressure zones (compressions) and low pressure zones (rarefactions). The molecules act just like the individual coils in the spring. The faster the molecules move back & forth, the greater the frequency of the wave, and the greater distance they move, the greater the wave’s amplitude.
Animation
rarefaction compression
molecule
Pressure vs. Position
The pressure at a given point in a medium fluctuates slightly as sound waves pass by. The wavelength is determined by the distance between consecutive compressions or consecutive rarefactions. At each com- pression the pressure is a tad bit higher than its normal pressure. At each rarefaction the pressure is a tad bit lower than normal. Let’s call the equilibrium (normal) pressure P 0 and the difference in pressure from equilibrium P. P varies and is at a max at a compression or rarefaction. In a fluid like air or water, Pmax is typically very small compared to P 0 but our ears are very sensitive to slight deviations in pressure. The bigger P is, the greater the amplitude of the sound
B
P
x A C
A: P = 0; P = P 0
B: P > 0; P = Pmax
C: P < 0; P = Pmin
animation
Pressure vs. Time Graph P (^) T
t
Rather than looking at a region of space at an instant in time, here we’re looking at just one point in space over an interval of time. At time zero, when the pressure readings began, the molecules were at their normal pressure. The pressure at this point in space fluctuates sinusoidally as the waves pass by: normal high normal low normal. The time needed for one cycle is the period. The higher the frequency, the shorter the period. The amplitude of the graph represents the maximum deviation from normal pressure (as it did on the pressure vs. position graph), and this corresponds to loudness. Docsity.com
Comparison of Pressure Graphs
Pressure vs. Position: The graph is for a snapshot in time and displays pressure variation for over an interval of space. The distance between peaks on the graph is the wavelength of the wave.
Pressure vs. Time: The graph displays pressure variation over an interval of time for only one point in space. The distance between peaks on the graph is the period of the wave. The reciprocal of the period is the frequency.
Both Graphs: Sound waves are longitudinal even though these graphs look like transverse waves. Nothing in a sound wave is actually waving in the shape of these graphs! The amplitude of either graph corresponds to the loudness of the sound. The absolute pressure matters not. For loudness, all that matters is how much the pressure deviates from its norm, which doesn’t have to be much. In real life the amplitude would diminish as the sound waves spread out.
F μ
v =
B v =
Notice that each equation is in the form
The bulk modulus for air is tiny compared to that of water, since air is easily compressed and water nearly incompressible. So, even though water is much denser than air, water is so much harder to compress that sound travels over 4 times faster in water. Steel is almost 8 times denser than water, but it’s over 70 times harder to compress. Consequently, sound waves propagate through steel about 3 times faster than in water, since (70 / 8) 0.5^ 3.
v =
elastic property inertial property
Depending on temp, sound travels around 750 mph, which would be Mach 1. Twice this speed would be Mach 2, which is about the max speed for the F-22 Raptor.
Speed Racer drives a car called ―The Mach 5,‖ which would imply it can go 5 times the speed of sound.
Some waves are one dimensional, like vibrations in a guitar string or sound waves traveling along a metal rod. Some waves are two dimensional, such as surface water waves or seismic waves traveling along the surface of the Earth. Some waves are 3-D, such as sound traveling in all directions from a bell, or light doing the same from a flashlight. To visualize 2-D and 3-D waves, we often draw wavefronts. The red wavefronts below could represent the crest of water waves on a pond moving outward after a rock was dropped in the middle. They could also be used to represent high pressure zonesin sound waves. The wavefronts for 3-D sound waves would be spherical, but concentric circles are often used to simplify the picture. If the wavefronts are evenly spaced, then is a constant.
AnimationDocsity.com
Just as the amplitude of a sound wave relates to its loudness, the frequency of the wave relates to its pitch. The higher the pitch, the higher the frequency. The frequency you hear is just the number of wavefronts that hit your eardrums in a unit of time. Wavelength doesn’t necessarily correspond to pitch because, even if wavefronts are very close together, if the wave is slow moving, not many wavefronts will hit you each second. Even in a fast moving wave with a small wavelength, the receiver or source could be moving, which would change the frequency, hence the pitch.
Frequency Pitch
Amplitude Loudness
Listen to a pure tone (up to 1000 Hz)
Listen to 2 simultaneous tones (scroll down) Docsity.com
Range of Human Hearing
Hear the full range of audible frequencies (scroll down to speaker buttons)
The maximum range of frequencies for most people is from about 20 to 20 thousand hertz. This means if the number of high pressure fronts (wavefronts) hitting our eardrums each second is from 20 to 20 000, then the sound may be detectable. If you listen to loud music often, you’ll probably find that your range (bandwidth) will be diminished.
Some animals, like dogs and some fish, can hear frequencies that are higher than what humans can hear (ultrasound). Bats and dolphins use ultrasound to locate prey (echolocation). Doctors make use of ultrasound for imaging fetuses and breaking up kidney stones. Elephants and some whales can communicate over vast distances with sound waves too low in pitch for us to hear (infrasound).
Animation
An echo is simply a reflected sound wave. Echoes are more noticeable if you are out in the open except for a distant, large object. If went out to the dessert and yelled, you might hear a distant canyon yell back at you. The time between your yell and hearing your echo depends on the speed of sound and on the distance to the to the canyon. In fact, if you know the speed of sound, you can easily calculate the distance just by timing the delay of your echo.
Reverberation is the repeated reflection of sound at close quarters. If you were to yell while inside a narrow tunnel, your reflected sound waves would bounce back to your ears so quickly that your brain wouldn’t be able to distinguish between the original yell and its reflection. It would sound like a single yell of slightly longer duration.
Animation (click on “The Doppler Effect”, then click on the button marked:
A tone is not always heard at the same frequency at which it is emitted. When a train sounds its horn as it passes by, the pitch of the horn changes from high to low. Any time there is relative motion between the source of a sound and the receiver of it, there is a difference between the actual frequency and the observed frequency. This is called the Doppler effect. Click to hear effect:
The Doppler effect applied to electomagnetic waves helps meteorologists to predict weather, allows astronomers to estimate distances to remote galaxies, and aids police officers catch you speeding.
The Doppler effect applied to ultrasound is used by doctors to measure the speed of blood in blood vessels, just like a cop’s radar gun. The faster the blood cell are moving toward the doc, the greater the reflected frequency.
Wavefront Animations Another cool animation
Animation with sound (click on ―The Doppler Effect‖, then click on the button marked:
Movie: F-18 Hornet breaking the sound barrier (click on MPEG movie)
When a source of sound is moving at the speed of sound, the wavefronts pile up on top of each other. This makes their combined amplitude very large, resulting in a shock wave and a sonic boom. At supersonic speeds a ―Mach cone‖ is formed. The faster the source compared to sound, the smaller the shock wave angle will be.
