Review L 23 – Vibrations and Waves [3] • A mechanical wave is a disturbance that resonance travels through a medium – solids, liquids or clocks – pendulum gases springs harmonic motion • The disturbance moves because of the mechanical waves elastic nature of the material sound waves • As the disturbance moves, the parts of the golden rule for waves material (segment of string, air molecules) musical instruments execute harmonic motion (move up and The Doppler effect down or back and forth) – Doppler radar – transverse wave – radar guns – radar guns – longitudinal wave
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transverse wave on a string Slinky waves
• you can create a longitudinal wave on a slinky • instead of jiggling the • jiggle the end of the string to create a disturbance slinky up and down, • the disturbance moves down the string you jiggle it in and out • as it passes, the string moves up and then down • the coils of the slinky •the string motion in vertical but the wave moves in the move along the same horizontal (perpendicular) directionÎ transverse wave direction (horizontal) • this is a single pulse wave (non-repetitive) as the wave • the “wave” in the football stadium is a transverse wave
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Harmonic waves watching the waves go by
• continually jiggle the end of the string up and down • suppose we keep watching one segment of the string as • each segment of the string undergoes simple harmonic the wave goes by and then make a plot of its motion motion and the disturbance (wave) moves with speed v • the time between the appearance of a new wave crest is • the distance between successive peaks is called the the PERIOD of the wave, T WAVELENGTH, λ (lambda) measured in m or cm • the number of wave crests that pass by every second is the wave frequency, f = 1/T v
λ λ time displacement snapshot of the string at some time sit at some x 5 and watch T T 6
1 The golden rule for waves Example: wave on a string
• the speed of propagation of the wave (v), the wavelength (λ), and period (T) are related • distance = speed x time Æ λ = v T = v / f • The wavelength = wave speed / frequency 2 cm 2 cm 2 cm or Æ v = λ×f Å (golden rule) • Wave speed = wavelength × frequency • A wave moves on a string at a speed of 4 cm/s • This applies to all waves Æ water waves, • A snapshot of the motion reveals that the waves on strings, sound, radio, light . . wavelength(λ) is 2 cm, what is the frequency (ƒ)? • This rule is important for understanding how •v = λ׃, so ƒ = v / λ = (4 cm/s ) / (2 cm) = 2 Hz musical instruments work 7 8
Sound – a longitudinal wave SOUND WAVES
• longitudinal pressure disturbances in a gas • the air molecules jiggle back and forth in the same direction as the wave • a sound wave is a pressure “disturbance” that • with no air molecules moves the through air (or other gas or liquid) to juggle, there is no • the “disturbance” is a change in the air pressure the diaphragm of the sound , e.g. in (increase or decrease) compared to its normal vacuum value (atmospheric pressure) speaker moves in and • it is a longitudinal wave out 9 10
The speed of sound Why do I sound funny when I breath helium? • SoundÆ pressure waves in a gas, liquid • Sound travels twice as fast in helium, or solid because Helium is lighter than air • Remember the golden rule v = λ׃ • The speed of soundÆ vs s • Air at 20 C: 343 m/s = 767 mph ≈ 1/5 mile/sec • The wavelength of the sound waves you • Water at 20 C: 1500 m/s make with your voice is fixed by the size of • copper: 5000 m/s your mouth and throat cavity.
• Depends on density and temperature • Since λ is fixed and vs is higher in He, the frequencies of your sounds is twice as high in helium! 5 second rule for thunder and lightening 11 12
2 Tuning forks make sound waves Vibration modes of a string
• The vibration of the fork causes the air near it to NNA Fundamental mode vibrate Wavelength = 2 L Frequency = f • The size of the fork L o determines the frequency – bigger fork Æ lower f A –smaller fork Æ higher f N A N N First harmonic mode • It produces a pure pitchÆ Wavelength = L
single frequency L Frequency = 2 fo
13 N = nodes, A = antinodes 14
Standing waves Vibration frequencies
• At the NODE positions, the string does not • In general, f = v / λ, where v is the move propagation speed of the string • At the ANTINODES the string moves up • The propagation speed depends on the and down harmonically diameter and tension • Only certain wavelengths can fit into the • Modes
distance L – Fundamental: fo = v / 2L
• The frequency is determined by the – First harmonic: f1 = v / L = 2 fo velocity and mode number (wavelength) • The effective length can be changed by the musician “fingering” the strings 15 16
Stringed instruments Organ pipes • The air pressure inside the • Three types pipe can vibrate, in some – Plucked: guitar, bass, harp, harpsichord places it is high and in other – Bowed: violin, viola, cello, bass places low – Struck: piano • Depending on the length of the pipe, various resonant • All use strings that are fixed at both ends modes are excited, just like – Use different diameter strings (mass per unit blowing across a pop bottle length is different) • The long pipes make the low – The string tension is adjustable - tuning notes, the short pipes make the high notes 17 18
3 Beats – wave interference • Waves show a special property called interference • When two waves are combined together, the waves can add or subtract • We call this constructive and destructive interference • When a wave is launched on a string it can reflect back from the far end. The reflected wave can combine with the original wave to make a standing wave 19 20
Constructive interference Destructive interference
waves add to give 0 amplitude Waves add to double amplitude
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Combining 2 waves of the same frequency Standing waves • standing waves are produced by wave interference • when a transverse wave is launched on a string a reflected wave is produced at the other end • the incident and reflected waves interfere with each other to produce a standing wave
Red + Blue
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4 Combining 2 waves of slightly different frequencies Room Acoustics
• Destructive interference accounts for bad room acoustics
• Sound that bounces off a wall can interfere destructively (cancel out) sound from the speakers resulting in dead spots
Red + Blue Beats 25 26
Wave interference can be used to eliminate noise –anti-noise technology A science teacher demonstrating the Doppler effect
ÆIf the source of sound moves toward you, you hear a higher frequency (pitch) sound.
Æ If the source of sound moves away from you, you hear a lower frequency sound.
Take one wave, turn it upside down (invert its phase) then add it to the original wave 27 28
Doppler effect Æ Radar guns Once you see the cop, he’s got you!
When radar waves bounce off a moving object (echo )the frequency of the reflected radar changes by an amount that depends on how fast the object is moving. The detector senses the frequency shift and translates this into a speed.
http://auto.howstuffworks.com/radar-detector1.htm 29 30
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