principle of superposition

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Principle of Superposition The displacements of overlapping waves add algebraically.* y TOT (x,t) = y 1 (x,t) + y 2 (x,t) Interfering pulses (* Only if the restoring force obeys Hooke’s law.)

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Principle of Superposition. The displacements of overlapping waves add algebraically.* y TOT (x,t) = y 1 (x,t) + y 2 (x,t) Interfering pulses (* Only if the restoring force obeys Hooke’s law.). Interference of Waves - different phase constants. Interference of Waves - different frequencies. - PowerPoint PPT Presentation

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Page 1: Principle of Superposition

Principle of Superposition

The displacements of overlapping waves add algebraically.*

yTOT(x,t) = y1(x,t) + y2(x,t)

Interfering pulses

(* Only if the restoring force obeys Hooke’s law.)

Page 2: Principle of Superposition

Interference of Waves - different phase constants

Page 3: Principle of Superposition

Interference of Waves - different frequencies

Animation 2 courtesy of Dan Russell, Kettering Univ.

Animation 1 - B.Surendranath Reddy

Page 4: Principle of Superposition

Fourier Series

Fourier Applet

Website

Page 5: Principle of Superposition

Wave Reflections

Page 6: Principle of Superposition

Exam Note Card Rules:

• One 5-inch by 8-inch note card may be used, front and back.

• The top line of the note card must contain your full name and course number (legibly written) and nothing else.

• Excepting the top line, only equations may be written on the card. Do not write concepts, terminology, names of variables; do not draw figures, etc.

• The equations must stand alone. For example, do not work out homework problems or write anything resembling a derivation.

• The material is to be hand-written, not typed.

• You must hand in your note card at the conclusion of the exam.

Page 7: Principle of Superposition

Sound Waves

Rays - indicate direction of wave propagation

Wavefronts - surfaces over which the wave displacement is equal(the distance between wavefronts is a wavelength)

Link

Rays are usually perpendicular to wavefronts

Page 8: Principle of Superposition

Speed of a Wave

Wave on a String

Medium?

1) Elastic property of the medium (to store P.E.)Depends on:€

v = Fμ

= Tensionmass/length

2) Inertial property of the medium (for K.E.)

Sound Wave Air

Elastic Property? Bulk Modulus,- defines the compressibility of the air- describes how change in pressure produces a fractional change in volume

Inertial Property? Density, €

B

ρ

v = Bρ

Page 9: Principle of Superposition

Does sound travel faster in air or water?

ρair = 1.2 kg/m3

ρwater = 1.0 g/cm3

v = Bρ = 1000 kg/m3

B = −ΔPΔVV

Relates the Pressure that produces a fractional change in Volume

What about Bulk Modulus?

So, does water or air require more pressure to achieve the same compression?

Bair = 1.41 x 105 N/m2

Bwater = 2.2 x 109 N/m2

vair = 343 m/s

vwater = 1483 m/s

Page 10: Principle of Superposition

Intensity Scales

Intensity (W/m2) Sound Level (dB)

Threshold of Hearing (I0) 10-12 0

Normal Conversation 10-6 60

Threshold of Pain 100 120

Define: Sound Level

Units: Decibels (dB)

β =10 log( II0

)

We can hear an extremely wide range of intensities (over 12 orders of magnitude!)

Page 11: Principle of Superposition

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Stationary Source

Page 12: Principle of Superposition

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

Start End

Moving Source - Doppler Effect

http://home.messiah.edu/~barrett/mpg/dopplerv_14.mpg

Link

Page 13: Principle of Superposition

Doppler Effect - Applications

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