Notes

Outline

Chapter 6 Waves and Sound By Ray Merry Back to home: www.raymerry.com Back to Physics: www.raymerry.com/classes/Physics

Waves in Action:

Wave A traveling disturbance consisting of coordinated vibrations that carry energy with no net movement of matter. See pages 217,218,219

Do the Wave! Have you ever "done the wave" as part of a large crowd at a football or baseball game? A group of people jump up and sit back down, some nearby people see them and they jump up, some people further away follow suit and pretty soon you have a wave traveling around the stadium. The wave is the disturbance (people jumping up and sitting back down), and it travels around the stadium. However, none of the individual people the stadium are carried around with the wave as it travels - they all remain at their seats.

Wave medium The wave medium is the substance the wave is traveling through. E.G. Sound requires a media or material to travel through.   The media can be water, air, wood, etc. Light on the other hand travels through a vacuum, and may not require a media.

Compare a wave pulse and a continuous wave. A wave pulse is one up and down or back and forth motion of a wave (short and fleeting). A continuous wave has many pulses (steady and repeating) .

Wave Pulse

Demonstrate both transverse and longitudinal waves on a Slinky, Transverse wave oscillations are perpendicular (transverse) to the direction the wave travels. (p. 219 fig. 6.4 a.) Longitudinal wave oscillations are along the direction the wave travels. (p. 219 fig. 6.4 b.) note corrections in book p. 219 & 220

Examples of Waves and Their Type Longitudinal, Sound in air Transverse, fan wave, sea wave.

Speed of a wave on a rope depends on its mass density and the tension applied. r = greek letter rho, stands for linear density r=  linear mass density of a rope, string, etc.  = m/l  (mass/length) v= (F/r)½  (Speed of a wave on a rope, etc. = sq. rt. of Force/linear density.)

Compute the speed of sound in air given the temperature. V= 20.1x(T)1/2  (20.1 x sq.rt of Temp in Kelvins) Speed of sound waves in air at temperature T (SI units, T in Kelvins)

Wavelength and Amplitude Amplitude: Maximum displacement of points on a wave, measured from the equilibrium position. Wavelength: (l) The distance between two successive "like" points on a wave. An example is the distance between two adjacent peaks or two adjacent valleys. See fig.6.5 p221

Wavelength vs Amplitude Figure

Frequency of a Wave The number of cycles of a wave passing a point per unit time. It equals the number of oscillations per second of the wave. If 15 waves pass a point in 1 second the frequency f = 15 Hz.

Wave Equation Equation relating the velocity, v, frequency, f, and wavelength, l, of a continuous wave. V=fl velocity of waves = frequency x wavelength

Wavefronts and Rays. See p 225 fig. 6.11 & fig 6.12 and p 226 fig. 6.14

Amplitude of a wave gets smaller farther from the source. The wave energy spreads out in 3 dimensions, like the surface of a sphere. As a result the same energy is spread out over a larger and larger surface and amplitude decreases.

Define a plane wave. A wave so far from it’s source that the wave front appears to be a straight line.

Give concrete examples of reflection of waves. Echoes. Parabolic Antennas

Doppler effect The apparent change in frequency of a wave due to motion of the source of the wave, the receiver, or both.

Effects of Movement on f and λ If the source is moving towards the observer, the observer perceives sound waves reaching him or her at a more frequent rate (high pitch) If the source is moving away from the observer, the observer perceives sound waves reaching him or her at a less frequent rate (low pitch).

Consequences of the Doppler effect. pitch of an ambulance or police siren, goes up as it approaches and then goes down as it recedes from you Same effect from a passing train whistle. Used in astronomy to deduce the component of velocity in the line-of-sight of an approaching or receding planet/star/galaxy etc.

How it was discovered that the universe is expanding. Doppler effect was used to determine speed of galaxies. They were all found to be moving away from the center The farther away they were the faster they seemed to be going away!

Cosmology The study of the structure and evolution of the universe as a whole.

Hubble relation (or law) A mathematical expression showing that the farther a galaxy is from us, the faster it is moving away. One implication of this relation is that the universe is expanding.

Echolocation: Radar, Sonar… Process of using the reflection of a wave to locate objects. We send out a wave, wait for its return. Since we know the speed and the time, from d=v x t we determine its distance away

Explain what causes a sonic boom. Sound waves build up in front as plane, etc. approaches the speed of sound.  When it passes the speed of sound they are left behind. Similar to bow waves on a boat.

Diffraction The bending of a wave as it passes around the edge of a barrier. Diffraction causes a wave passing through a gap or a slit to spread out into the shadow regions. See fig. 6.26 p. 232

Examples of Diffraction Sound waves traveling around corners Water waves going through openings.

Interference The consequence of two waves arriving at the same place and combining. See fig. 6.28 p. 233

Constructive interference occurs wherever the two waves meet in phase (peak matches peak); the waves add together.

Destructive interference Destructive interference occurs wherever the two waves meet out of phase (peak matches valley); the waves cancel each other.

Phase and Interference Give an explanation of how the phase relationship of superposed waves determines whether they interfere constructively or destructively. In phase is constructive, out of phase 180 degrees (half a cycle) is destructive.

What is sound? A wave disturbance which our ears are sensitive to.  A longitudinal wave in air, if it is audible it has a frequency between 20 and 20,000 hz. Does sound occur if there is no one to hear it?

Sound The back and forth vibrations of the surrounding air molecules creates a pressure wave which travels outward from its source. This pressure wave consists of compressions and rarefactions. The compressions are regions of high pressure, where the air molecules are compressed into a small region of space. The rarefactions are regions of low pressure, where the air molecules are spread apart. This alternating pattern of compressions and rarefactions is known as a sound wave.

Sound From a String

Reaction of the Air The back and forth vibrations of the surrounding air molecules creates a pressure wave which travels outward from its source. This pressure wave consists of compressions and rarefactions.

Sound Wave The compressions are regions of high pressure, where the air molecules are compressed into a small region of space. The rarefactions are regions of low pressure, where the air molecules are spread apart. This alternating pattern of compressions and rarefactions is known as a sound wave.

Pitch How high or low a sound is, related to the frequency of the sound. Higher pitches have higher frequency waves.

Decaying Sound

Reverberation

Ultrasound Very high frequency sound waves, higher than we can hear. Used in medicine in imaging and to destroy kidney stones in the bladder

Applications of Sound Sonar Ultrasound Analysis Bats Echolocation Insect Repellant/Dog Whistle

Musical Scale 8 notes in the scale, key is the starting note  Key of C has CDEFGAB Notes repeat in octaves. One octave is double the frequency of the one below.

Pure tones, complex tones, and noise.

Beats Waves close in frequency sometimes constructively interfere, causing a sudden loudness. E.G. sound of 500 hz and 502 hz, 2 hz is the difference or beat frequency, 502 –500 = 2 Two times per second they would interfere constructively.

Musical Instruments Recognize some differences in the ways various musical instruments produce sound. wind instruments: blow reed vibrates percussion: stike and they vibrate strings: pluck or bow and they vibrate

Harmonics Harmonics are sounds emitted in simple ratios of the main or fundamental frequency First Harmonic or fundamental =  f Second H = 2f Third H= 3f, etc.

Harmonic Diagrams

Standing Wave Demo http://id.mind.net/~zona/mstm/physics/waves/standingWaves/standingWaves1/StandingWaves1.html

Superposition of Waves

Problem on Harmonics If a sound of A has 220 Hz, what are the first and third harmonics? 1st H = f = 1 x 220 = 220 Hz 2nd H = 2 x f, third = 3 x f = 3 x 220 = 660Hz

Loudness and Decibels A bel is a rating of the power of 10 of the amplitude of a wave.  E.g. 10, vs 100, = 1 bel more (101 vs. 102 ) which is 10 decibels Related to intensity of the sound.  Closest measurement is the decibel (.1 bel) Minimum difference in intensity we can hear is 1 db, to sound louder

Decibel Ratings 120 db  is the threshold of pain 2 identical sounds are 3 db higher than the single sound. It takes 10 identical sounds to sound twice as loud, which is a change of 10 db. This is cumulative, 100 db sounds 4x as loud as 80 db. Back to home: www.raymerry.com Back to Physics: www.raymerry.com/classes/physics

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