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Unit 6: Waves and Sound

Brent Royuk Phys-109

Concordia University

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Waves •  What is a wave? •  Examples

–  Water, sound, slinky, ER •  Transverse vs. Longitudinal

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Wave Properties •  The magic of waves.

–  Great distances –  What are they made of?

•  Wave Anatomy –  Crest, trough, speed, frequency, wavelength, amplitude.

•  The Wave Equation: v = fλ –  What is the wavelength of a sound wave produced by a

violin playing the note A above middle C when the speed of sound is 350 m/s?

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The Four Wave Behaviors 1.  Reflection

–  Waves bounce off obstacles 2.  Refraction

–  Waves bend when entering a new medium at an angle.

3.  Diffraction –  Waves bend around corners and spread out

from small openings.

4.  Superposition (Interference) –  Waves pass through each other, and

their amplitudes add.

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Superposition

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Constructive vs. Destructive Interference

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Interference

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Standing Waves

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Standing Waves • How are these waveforms

produced? • Consider a vibrating string:

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Standing Waves • Another view:

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Two-Source Interference

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Sound Waves •  All sound waves are longitudinal air waves created by vibrations.

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Sound Waves •  All sound waves are created by vibrations.

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Sound Waves •  Pushing air

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Speed of Sound

•  vsound = (331 + 0.606 TC) m/s

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Speed of Sound

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vw = 331m s( ) T273 K

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Speed of Sound •  vsound = (331 + 0.606 TC) m/s

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Speed of Sound •  vsound = (331 + 0.606 TC) m/s •  Misconception: Sonic boom is heard when vs is exceeded. •  So does a whip break the sound barrier?

–  The whip is tapered so transverse wave energy causes faster speeds.

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Speed of Sound

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Speed of Sound

Material Speed (m/s) Aluminum 6420 Granite 6000 Plastic 2680 Fresh Water (200 C) 1482 Fresh Water (00 C) 1402 Hydrogen 1284 Air (00 C) 331

•  Speed in different media: stiffer means faster

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The Sound Spectrum •  Infrasonic 0-20 Hz •  Audible 20 Hz-20 kHz •  Ultrasonic 20 kHz-1 GHz

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The Sound Spectrum

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The Sound Spectrum

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Sound Intensity •  I = Watts/m2

–  Point source obeys an inverse square law •  So double distance equals 1/4 as much, etc.

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Sound Intensity •  Threshold of hearing ≈ 10-12 W/m2, pain threshold ≈ 1 W/

m2 •  This is a big range, so we use a logarithmic scale: log I/

Io gives bels, where Io = threshold of hearing = 10-12 W/m2 –  1 dB = 0.1 B –  β = 10 log (I/Io)

•  The logarithmic scale also matches human sound perception.

•  Note that every 10 dB represents a 10x increase in sound –  How much louder is 80 dB than 60 dB?

•  Other logarithmic scales?

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Sound Intensity

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The Reflection of Sound •  Echoes •  Parabolic microphones •  Ultrasonic rangefinders •  Whispering galleries

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The Refraction of Sound •  Isotherms for submarines •  Thermal inversion/The lake effect

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The Diffraction of Sound

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The Doppler Effect

– means towards + means away

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Beats •  Turn signals analogy •  The beat frequency •  http://library.thinkquest.org/19537/

java/Beats.html

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Musical Sound •  Loudness = I

–  Equal loudness contours, next slide •  Pitch = f, wavelength

–  well, almost: also depends on loudness, different for different frequencies

•  Timbre, quality = waveform –  composed of pure tones

•  Waveforms: tuning fork vs. guitar –  Harmonics (on guitar): overtones –  Different instruments have different overtones, thus

different timbre •  e.g. closed pipes only have even overtones, duller

than open pipes •  Different resonators: wind, string, percussion

comparisons

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Equal Loudness Contours

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Timbre •  aka Quality, Color: The characteristic tone distinctive of

a particular singing voice or musical instrument •  Physical difference: Waveform

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Overtones

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Dissecting the Waveform

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Overtone Series

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Harmony •  Integral multiples of a frequency reinforce each

other •  The harmonic series

–  128 C below middle C –  256 middle C –  384 G above middle C –  512 C above middle C –  640 E –  768 G –  896 B flat –  1024 C again

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Resonance •  Resonance tubes •  Singing rods •  Resonant room frequencies

–  A room's fundamental resonant frequency can be calculated by dividing the speed of sound in feet per second (1130) by twice the length.

•  Chladni Plates: http://www.youtube.com/watch?v=Pfs4Rd5f_IQ

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Chladni Plates

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Resonance •  Tacoma Narrows Bridge Collapse

–  The first Tacoma Narrows Bridge opened to traffic on July 1, 1940. Its main span collapsed into the Tacoma Narrows four months later on November 7, 1940, at 11:00 AM (Pacific time) due to a physical phenomenon known as aeroelastic flutter caused by a 67 km/h (42 mph) wind. The bridge collapse had lasting effects on science and engineering. In many undergraduate physics texts the event is presented as an example of elementary forced resonance with the wind providing an external periodic frequency that matched the natural structural frequency (even though the real cause of the bridge's failure was aeroelastic flutter).

–  No human life was lost in the collapse of the bridge. However, a small do perished after it was abandoned in a car on the bridge by its owner, Leonard Coatsworth, and by another man, both of whom were bitten by the terrified dog when they attempted to remove it.

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Resonance •  Live room standing wave patterns