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