Unit 8 Waves and Sound
Jan 19, 2016
Unit 8
Waves and Sound
Simple Harmonic Motion
• Vibration - a disturbance in time. A periodic disturbance that occurs over time. – An object vibrating always tries to return to equilibrium
• simple harmonic motion Pendulum and mass on a spring and object moving in a circle
• http://www.walter-fendt.de/ph11e/springpendulum.htm
• http://www.walter-fendt.de/ph11e/pendulum.htm
Simple Harmonic Motion
• Simple Pendulum
g
LT 2
Variables
T = Period
g = Acceleration due to gravity
L = Length of the pendulum
Waves
• A disturbance in time (vibration) that moves through space
• Waves are a transfer of Energy not mass
Medium
• The material which a wave moves through– Some waves require a medium some don’t
• Examples: air, water, earth, strings, springs etc.
Types of Waves
• Mechanical Waves: (require a medium)Sound, earthquake, water, waves on a string, waves on a spring
• Electromagnetic Waves (do not require medium)Visible light, radio waves, x-rays, microwaves, gamma rays, ultraviolet, infrared
Pulse
• A single vibration traveling through a medium
• wave-on-a-string
Wave measurements
• Amplitude (A) max displacement of wave (amount of energy in the wave)
• Wavelength (λ) the distance covered by a wave in one oscillation
• Period (T) Time for one wave to pass
• Frequency (f) number of waves created in one second
Wave speed
• Wave speed: depends only on medium
• Velocity of a wave is constant in same medium, regardless of wavelength or frequency
Equation: ft
dv
Transverse waves
• Waves what vibrate the medium perpendicular to the wave (energy) motion
• Ex) light, earthquake s-waves, water,
http://www.kettering.edu/~drussell/Demos/wave-x-t/wave-x-t.html
http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html
Longitudinal Wave
• Wave that vibrates the medium parallel to the direction of the energy (wave) motion
• Ex) sound, earthquake p-waves
• http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html
Phase
• In Phase: points on a wave that are moving in the same direction with the same amplitude
• 180 degrees Out of phase: points moving in opposite direction with opposite amplitude
Boundary• A region between two mediums
– Transmission – energy moves through the boundary into a new medium
– Reflection – energy is bounced off the boundary back into the same medium
– Absorption- energy is kept by the boundary (usually turned to heat)
Reflection• Bouncing of a wave off a boundary back into
the original medium
• Fixed boundary – easily vibrated medium to rigid medium
• Unfixed boundary – rigid medium to easily vibrated medium
Waves changing mediums• When a wave is transmitted into a new medium
– The wave will change speed– The wave will change wavelength– The wave may change direction– The wave will not change frequency
Highest wave surfed 100ft = amplitude 50ft
Principal of Superposition
• The ability of two or more waves to exist in the same place at the same time.
• Waves pass through each other.
Constructive Interference
• Two waves in phase superimpose and add their amplitude’s together resulting in a larger wave.
http://phet.colorado.edu/simulations/stringwave/stringWave.swf
Destructive Interference
• Two waves that are 180o out of phase superimpose and add their amplitudes to result in a smaller wave
http://phet.colorado.edu/simulations/stringwave/stringWave.swf
Diffraction
-The ability of a wave to move around obstacles
-Larger wavelength results in more diffraction
Ripple tank
Small opening compared to the wavelength more diffraction
Large opening compared to the wavelength less diffraction
Sound
• Needs a medium
• Pitch- frequency of sound– Humans hear 20 Hz to 20,000 Hz
• Infrasound frequencies less than 20 Hz• Ultrasound frequencies greater than 20,000 Hz
• Loudness- Amplitude (amount of energy)– Measured in Decibels (dB)
Decibel Scale
• Near total silence - 0 dB
• A whisper - 15 dB
• Normal conversation - 60 dB
• A lawnmower - 90 dB
• A car horn - 110 dB
• A rock concert or a jet engine - 120 dB
• A gunshot or firecracker - 140 dB
Speed of Sound vs. Speed of Light
• Speed of sound depends on medium– vair = 345m/s at room temperature– vair = 331m/s at 0 degrees C
Equation: vair = 331m/s + 0.6(T)
– vwater = 1500m/s– vsteel = 5000m/s
• Speed of light (c) = 3x108m/s
Beats
• 2 waves with different frequencies interfere
• Moving interference pattern
• Forced Vibration: An object is forced to vibrate waves hitting it. Can be caused at any frequency.
Ex. Tuning fork on the table top.
Resonance
• A phenomenon where standing waves are created by energy being inputted into the medium at the Natural Frequency (Resonate Frequency) of the medium
• Natural Frequency: Frequency where the medium easily absorbs energy (creates a standing wave) or (Resonates)
Standing Waves
• When two waves superimpose that are 180 degrees out of phase, moving in opposite directions with the same wavelength and frequency they produce a standing wave interference pattern.
• The pattern is made up of alternating regions of constructive interference (antinodes) and destructive (nodes) interference
Types of standing waves
• Closed-Closed Pattern– Medium fixed at both ends
• Open-Open Pattern– Medium unfixed (open) at both ends
• Open-Closed Pattern– Medium fixed on one end and unfixed on
opposite end.
http://mysite.verizon.net/vzeoacw1/harmonics.html
1st harmonicL = 2/ג
2nd harmonicL = ג
3rd HarmonicL = 3/2 ג
4th HarmonicL = 2 ג
L
L
NN
N N N
A A
A
L
N N NA A
NA
L
N N NA A
NN
AA
Open-Open Standing Wave
1st harmonicL = 2/ג
2nd harmonicL = ג
3rd HarmonicL = 3/2 ג
4th HarmonicL = 2 ג
L
NAA
L
ANN
A
A
A
L
N N NA
A
A
L
AN NN
AN
AA
A
Open – Closed Standing wave
1st HarmonicL = λ/4
3rd HarmonicL = ¾ λ
5th HarmonicL = 5/4 λ
7th HarmonicL = 7/4 λ
L
N
N
A
L
N
A
A
L
N N NA
A A
LN N N
AN
A
A
A
Example: Draw the 6th harmonic of standing wave in a pipe open on both ends.
L = 3λ
1m = 3λ
λ = ?
λ = .33m
v = f*λ
345m/s = f*(.33m)
f = ?
f = 1035Hz
If the pipe is 1 meter long what is the wavelength of the wave?
Find the frequency of the wave if the speed of the sound wave is 345 m/s.
Doppler Effect
• If the source of a wave and an observer are moving together the observed frequency of the wave will be higher and the wavelength shorter
• If the source of wave and an observer are moving apart the observed frequency of the wave will be lower and the wavelength longer
Doppler Shift
• With sound the observer hears a higher pitch if source and observe come together and a lower pitch if they move apart
• With light the observer will see a blue shift in the color if they are coming together and red shift if they are moving apart
Happy Birthday
• Melody C C D C F E• Harmony A A Bb
• Melody C C D C G F• Harmony Bb Bb A
• Melody C C C A F E D• Harmony F C Bb
• Melody Bb Bb A F G F• Harmony C A