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Waves

Waves. Overview (Text p382>). Waves – What are they?. Imagine dropping a stone into a still pond and watching the result. A wave is a disturbance that transfers energy from one point to another in wave fronts. Examples Ocean wave Sound wave Light wave Radio wave .

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Waves

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  1. Waves Overview (Text p382>)

  2. Waves – What are they? • Imagine dropping a stone into a still pond and watching the result. • A wave is a disturbance that transfers energy from one point to another in wave fronts. • Examples • Ocean wave • Sound wave • Light wave • Radio wave

  3. Waves – Basic Characteristics • Frequency (f) cycles/sec (Hz) • Period (T) seconds • Speed (v) meters/sec • Amplitude (A) meters • Wavelength () meters • Peak/Trough • Wave spd = w/length * freq • v =  * f

  4. Wave – Basic Structure

  5. Wave Types • 2 types of waves: • Electromagnetic • Require NO medium for transport • Speed is speed of light @ 3 x 108 m/s • Examples – light, radio, heat, gamma • Mechanical • Require a medium for transport of energy • Speed depends on medium material • Examples – sound, water, seismic

  6. Waves – Electromagnetic • Wave speed is 3 x 108 m/s • Electric & Magnetic fields are perpendicular

  7. Waves – Radio • Electromagnetic type • Most radio waves are broadcast on 2 bands • AM – amplitude modulation (550-1600 kHz) • Ex. WTON 1240 kHz • FM – frequency modulation (86 – 108 MHz) • Ex. WMRA 90.7 MHz • What are their respective wavelengths?

  8. Practice • What is the wavelength of the radio carrier signal being transmitted by WTON @1240 kHz? • Solve c = λ*f for λ. • 3e8 = λ * 1240e3 • λ = 3e8/1240e3 = 241.9 m

  9. Practice • What is the wavelength of the radio carrier signal being transmitted by WMRA @ 90.7 MHz? • Solve c = λ*f for λ. • 3e8 = λ * 90.7e6 • λ = 3e8/90.8e6 = 3.3 m

  10. Mechanical Waves • 2 types of mechanical waves • Transverse • “across” • Longitudinal • “along”

  11. Waves – Mechanical Transverse • Transverse • Particles move perpendicularly to the wave motion being displaced from a rest position • Example – stringed instruments, surface of liquids >> Direction of wave motion >>

  12. Waves - Mechanical Longitudinal • Particles move parallel to the wave motion, causing points of compression and rarefaction • Example - sound >> Direction of wave motion >>

  13. Longitudinal Waves

  14. Sound • Speed of sound in air depends on temperature • Vs= 331 + 0.6(T) above 0˚C • Ex. What is the speed of sound at 20°C? • Ss = 331 + 0.6 x 20 = 343 m/s • Speed of sound also depends upon the medium’s density & elasticity. In materials with high elasticity (ex. steel 5130 m/s) the molecules respond quickly to each other’s motions, transmitting energy with little loss. • Other examples – water (1500), lead (1320) hydrogen (1290) Speed of sound = 340 m/s (unless other info is given)

  15. Sounds and humans • Average human ear can detect & process tones from • 20 Hz (bass – low frequencies) to • 20,000 Hz (treble – high frequencies)

  16. Doppler Effect • What is it? • The apparent change in frequency of sound due to the motion of the source and/or the observer.

  17. Doppler Effect • Moving car example

  18. Doppler Effect Example • Police radar

  19. Doppler Effect Formula • f’ = apparent freq • f = actual freq • v = speed of sound • vo = speed of observer (+/- if observer moves to/away from source) • vs = speed of source (+/- if source moves to/away from the observer) • Video example

  20. Sound Barrier #1

  21. Sound Barrier #2 THRUST SSC LSR: 763 mph or 1268 km/hr

  22. Doppler Practice • A police car drives at 30 m/s toward the scene of a crime, with its siren blaring at a frequency of 2000 Hz. • At what frequency do people hear the siren as it approaches? • At what frequency do they hear it as it passes? (The speed of sound in the air is 340 m/s.)

  23. Doppler Practice • A car moving at 20 m/s with its horn blowing (f = 1200 Hz) is chasing another car going 15 m/s. • What is the apparent frequency of the horn as heard by the driver being chased?

  24. Interference of Waves • 2 waves traveling in opposite directions in the same medium interfere. • Interference can be: • Constructive (waves reinforce – amplitudes add in resulting wave) • Destructive (waves cancel – amplitudes subtract in resulting wave) • Termed - Superposition of Waves

  25. Superposition of Waves

  26. Superposition of Waves Special conditions for amp, freq and λ…

  27. Standing Wave? • A wave that results from the interference of 2 waves with the same frequency, wavelength and amplitude, traveling in the opposite direction along a medium. • There are alternate regions of destructive (node) and constructive (antinode) interference.

  28. Standing Wave

  29. Basic Terms • Harmonic number • n (1st, 2nd, 3rd, …) • Fundamental frequency • f1(n=1, 1st harmonic) • Nth harmonic frequency • fn = n * f1 • Length of string/pipe • L • Wave speed • v = 340 m/s in pipes 2 models for discussion…

  30. Standing Waves in Strings • Nodes occur at each end of the string • Harmonic # = # of envelopes • fn = nv/2L • f = frequency • n = harmonic # • v = wave velocity • L = length of string

  31. Standing Waves in Strings

  32. Practice • An orchestra tunes up by playing an A with fundamental frequency of 440 Hz. • What are the second and third harmonics of this note? • Solve fn = n*f1 • f1 = 440 • f2 = 2 * 440 = 880 Hz • f3 = 3 * 440 = 1320 Hz

  33. String Practice • A C note is struck on a guitar string, vibrating with a frequency of 261 Hz, causing the wave to travel down the string with a speed of 400 m/s. • What is the length of the guitar string? • Solve fn = nv/(2L) for L • L = nv/(2f) • L = 0.766 m

  34. Standing Waves in Open Pipes • Waves occur with antinodes at each end • fn = nv/2L • f = frequency • n = harmonic # • v = wave speed • L = length of open pipe

  35. Standing Waves in Pipes (closed at one end) • Waves occur with a node at the closed end and an antinode at the open end • Only odd harmonics occur • fn = nv/4L • f = frequency • n = harmonic # • v = wave speed • L = length of pipe

  36. Pipe Practice • What are the first 3 harmonics in a 2.45 m long pipe that is: • Open at both ends • Closed at one end • Solve • (open) fn = nv/(2L) find f1, f2, f3 • (closed @ 1 end) fn = nv/(4L) find f1, f3, f5

  37. Beats • Beats occur when 2 close frequencies (f1, f2) interfere • Reinforcementvscancellation • Pulsating tone is heard • Frequency of this tone is the beat frequency (fb) • fb = |f1 - f2|

  38. Beats f1 f2 |f1-f2| Ex. If f1 = 440 Hz and f2 = 420 Hz, then fb = (440-420) = 20 Hz

  39. Lab Practice • Simulation lab using EXPLORE • Standing Waves • Wave addition

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