# Vibrations & Waves & Sound a periodic motion of the particles of an elastic body or medium in alternately opposite directions from the position of equilibrium.

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Vibrations & Waves & Sound a periodic motion of the particles of an elastic body or medium in alternately opposite directions from the position of equilibrium when that equilibrium has been disturbed a periodic motion of the particles of an elastic body or medium in alternately opposite directions from the position of equilibrium when that equilibrium has been disturbed When things vibrate, they move the air and create sound waves When things vibrate, they move the air and create sound waves Music, talking, sirens, etc. Music, talking, sirens, etc.

Vibrations & Waves

Transverse Waves Wave Anatomy Wave Anatomy crest trough wavelength amplitude nodes

Vibrations & Waves Wavelength - Distance between peaks Wavelength - Distance between peaks Amplitude - Max Height above resting spot Amplitude - Max Height above resting spot Frequency - Number of Nodes-Crests- Troughs/second Frequency - Number of Nodes-Crests- Troughs/second Period - Time of a complete vibration Period - Time of a complete vibration Period = 1 / Frequency Period = 1 / Frequency Frequency = 1 / Period Frequency = 1 / Period

Vibrations & Waves Water Waves – bounce swimmers up and down Water Waves – bounce swimmers up and down Sound Waves - move air back and forth Sound Waves - move air back and forth

Wave Motion Consider a pebble thrown in the water Consider a pebble thrown in the water Creates circular waves that move out from the disturbance Creates circular waves that move out from the disturbance Water moves up and down, the wave moves outward away from the disturbance Water moves up and down, the wave moves outward away from the disturbance Waves carry energy from the impact Waves carry energy from the impact A bug in the water will move and and down A bug in the water will move and and down

Wave Speed Wavelength is distance between peaks Frequency is number of peaks per second going past a point in the water Frequency depends on wavelength and how fast the wave moves!!! Speed = Wavelength x Frequency

Longitudinal or Transverse?

Longitudinal Waves Wave Anatomy Wave Anatomy rarefaction compression wavelength

Sound Waves

Human Hearing sound wave vibrates ear drum amplified by bones converted to nerve impulses in cochlea

Sound Waves Molecules in the air vibrate about some average position creating the compressions and rarefactions. We call the frequency of sound the pitch.

Human Hearing Pitch Pitch highness or lowness of a sound highness or lowness of a sound depends on frequency of sound wave depends on frequency of sound wave human range: 20 - 20,000 Hz human range: 20 - 20,000 Hz ultrasonic waves subsonic waves

B. Human Hearing Intensity Intensity volume of sound volume of sound depends on energy (amplitude) of sound wave depends on energy (amplitude) of sound wave measured in decibels (dB) measured in decibels (dB)

Human Hearing 70 80 100 110 120 40 18 10 0 DECIBEL SCALE

Sound Waves

Speed of Sound Depends on the material of the vibrating medium Depends on the material of the vibrating medium Sound can vibrate water, wood (speaker enclosures, pianos), metal, plastic, etc. Sound can vibrate water, wood (speaker enclosures, pianos), metal, plastic, etc. Sound speed in dry air is 330 meters/second at 0 o C Sound speed in dry air is 330 meters/second at 0 o C Faster in warm air, slower in cold Faster in warm air, slower in cold Water 4 times faster, steel 15 times faster Water 4 times faster, steel 15 times faster

Wave Reflection When a sound wave reflects from a surface we generate an echo When a sound wave reflects from a surface we generate an echo Wave reflection from surfaces depends on the characteristics of the surface Wave reflection from surfaces depends on the characteristics of the surface Smooth hard surfaces reflect best Smooth hard surfaces reflect best Rough soft surfaces reflect poorly Rough soft surfaces reflect poorly Energy not reflected is absorbed or transmitted through the material Energy not reflected is absorbed or transmitted through the material

Wave Reflection Think of arrows pointing in the direction of the wave motion Think of arrows pointing in the direction of the wave motion We can trace the path of these arrows We can trace the path of these arrows Angles Equal

Wave Reflection Acoustics of room design is very interesting. Need some reflections to liven the room. Too many reflections and the sound gets mushy. Look in a concert hall or auditorium to see the different sound treatments

Wave Refraction If there is a change in the characteristics of a medium, waves are bent If there is a change in the characteristics of a medium, waves are bent This occurs because different parts of the wave front travel at different speeds This occurs because different parts of the wave front travel at different speeds Think of a marching around a curved track Think of a marching around a curved track The inside people have to move more slowly than the outside people to keep the lines straight The inside people have to move more slowly than the outside people to keep the lines straight

Wave Refraction

Wave Reflection & Refraction The combination of reflection and refraction enables imaging The combination of reflection and refraction enables imaging Ultrasonic medical imaging Ultrasonic medical imaging Naval SONAR for detecting submarines Naval SONAR for detecting submarines Bats catch mosquitoes Bats catch mosquitoes Catch discussion of dolphins on p. 261 Catch discussion of dolphins on p. 261

Natural Frequencies Objects have natural frequencies based on their size and structure Objects have natural frequencies based on their size and structure Guitar strings are an example Guitar strings are an example Timpani heads Timpani heads Air columns Air columns

Forced Vibrations Can externally impose a vibration on an object Can externally impose a vibration on an object Guitars and violins and pianos Guitars and violins and pianos Set the wood into motion at the frequency of the string Set the wood into motion at the frequency of the string This provides a larger surface to interact with the air This provides a larger surface to interact with the air Harp vs. Piano Harp vs. Piano

Resonance When the forced vibration matches a natural frequency we get a resonance condition When the forced vibration matches a natural frequency we get a resonance condition Think about a swing on a playground Think about a swing on a playground You go high when you pump the swing at its natural vibration frequency You go high when you pump the swing at its natural vibration frequency Sympathetic vibrations in tuning forks Sympathetic vibrations in tuning forks Famous Tacoma Narrows bridge collapse Famous Tacoma Narrows bridge collapse

Next Time We continue the chapter on waves and sound. We continue the chapter on waves and sound.

Wave Interference Principle of Superposition Principle of Superposition Works for both longitudinal waves and for transverse waves Works for both longitudinal waves and for transverse waves

Wave Interference Simply align the waves in time and add the amplitudes Simply align the waves in time and add the amplitudes Amplitudes can be either positive or negative Amplitudes can be either positive or negative If the amplitudes are of the same sign, the wave is reinforced and grows bigger If the amplitudes are of the same sign, the wave is reinforced and grows bigger If the amplitudes are of opposite sign, the wave is diminished and grows smaller If the amplitudes are of opposite sign, the wave is diminished and grows smaller

Wave Interference

So far, we have only looked at waves that have the same wavelength or frequency So far, we have only looked at waves that have the same wavelength or frequency What happens if the frequencies are different? What happens if the frequencies are different? According to the Superposition Principle, we simply add the two waves together to see what results According to the Superposition Principle, we simply add the two waves together to see what results

Wave Interference Produces Beats Produces Beats This is how musicians tune their instruments to match in the orchestra This is how musicians tune their instruments to match in the orchestra

Wave Interference 10% Frequency Difference 20% Frequency Difference

Standing Waves

C. Doppler Effect Doppler Effect Doppler Effect change in wave frequency caused by a moving wave source change in wave frequency caused by a moving wave source moving toward you - pitch sounds higher moving toward you - pitch sounds higher moving away from you - pitch sounds lower moving away from you - pitch sounds lower

Doppler Effect

Wave Barriers The object is moving at the speed of waves in the medium. See how the waves pile up at the source.

Shock Waves The source is moving faster than the wave speed in the medium. A shock wave is formed and it is very difficult to break through the previous wave barrier. These waves produce sonic booms.

Music vs. Noise Music Music specific pitches and sound quality specific pitches and sound quality regular pattern regular pattern Noise Noise no definite pitch no definite pitch no set pattern no set pattern

Guitar Strings

A combination wave composed of the 1st harmonic and the third harmonic.

Music What makes instruments unique is the combination of harmonics produced by the different instruments. What makes instruments unique is the combination of harmonics produced by the different instruments. Flutes produce primarily the 1st harmonic Flutes produce primarily the 1st harmonic They have a very pure tone They have a very pure tone Oboes produce a broad range of harmonics and sound very different Oboes produce a broad range of harmonics and sound very different

Combining Waves Revisited

Combining Waves

Musical Instruments Three ways to make sound Three ways to make sound Vibrate a string Vibrate a string Vibrate an air column Vibrate an air column Vibrate a membrane Vibrate a membrane

Vibrating Strings Violin, viola, cello, string bass Violin, viola, cello, string bass Guitars Guitars Ukuleles Ukuleles Mandolins Mandolins Banjos Banjos All vibrate a structure to amplify the sound All vibrate a structure to amplify the sound

Vibrating Air Columns Pipe Organs Pipe Organs Brass Instruments Brass Instruments Woodwinds Woodwinds Whistles Whistles

Vibrating Membranes Percussion Instruments Percussion Instruments Snare Drum Snare Drum Bass Drum Bass Drum Bongos Bongos Timpani are unique in that they are tuned to produce particular 1st harmonics Timpani are unique in that they are tuned to produce particular 1st harmonics You see the timpanist tunes each drum during a performance You see the timpanist tunes each drum during a performance

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