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Principle of Superposition

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.

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Principle of Superposition

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  1. 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.)

  2. Interference of Waves - different phase constants

  3. Interference of Waves - different frequencies Animation 1 - B.Surendranath Reddy Animation 2 courtesy of Dan Russell, Kettering Univ.

  4. Fourier Series Fourier Applet Website

  5. Wave Reflections

  6. 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.

  7. Sound Waves Rays - indicate direction of wave propagation Wavefronts - surfaces over which the wave displacement is equal (the distance between wavefronts is a wavelength) Rays are usually perpendicular to wavefronts Link

  8. Speed of a Wave Wave on a String Depends on: 1) Elastic property of the medium (to store P.E.) 2) Inertial property of the medium (for K.E.) Sound Wave Medium? 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,

  9. Does sound travel faster in air or water? air = 1.2 kg/m3 = 1000 kg/m3 water = 1.0 g/cm3 What about Bulk Modulus? Relates the Pressure that produces a fractional change in Volume So, does water or air require more pressure to achieve the same compression? vair = 343 m/s Bair = 1.41 x 105 N/m2 Bwater = 2.2 x 109 N/m2 vwater = 1483 m/s

  10. Intensity Scales We can hear an extremely wide range of intensities (over 12 orders of magnitude!) Define: Sound Level Units: Decibels (dB)

  11. Stationary Source

  12. Moving Source - Doppler Effect Start End http://home.messiah.edu/~barrett/mpg/dopplerv_14.mpg Link

  13. Doppler Effect - Applications

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