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Sect. 12-6: Sound Wave Interference & Beats

Sect. 12-6: Sound Wave Interference & Beats. Like any other waves, sound waves can interfere with each other. Example 12-12 Can lead to beats. Interference. Beats. An interesting & important example of interference is BEATS .

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Sect. 12-6: Sound Wave Interference & Beats

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  1. Sect. 12-6: Sound Wave Interference & Beats • Like any other waves, sound waves can interfere with each other. • Example 12-12 • Can lead to beats.

  2. Interference

  3. Beats • An interesting & important example of interference is BEATS. • Beats Two sound waves are close in frequency. They interfere with each other (Interference in time, instead of space!)  The sound level (intensity) alternately rises & falls.  “Eerie” Sounds!

  4. As a function of time, the two interfering waves (frequencies f2 & f1) alternately go through constructive & destructive interference. • Beat Frequency fB = f2 - f1

  5. Sect. 12-7: Doppler Effect • Observation: Pitch (frequency) of a sound changes when the source is moving & when the observer is moving. • Different effects when the source & the observer are moving away or coming towards each other.  THE DOPPLER EFFECT

  6. Doppler Effect

  7. In air, at rest, source frequency  f = 1/T, period T Speed of sound  v. Distance between crests: d = λ = vT . T = (λ/v) • Source movingTOWARDSobserver, speed  vs • In time T =1/f, source moves a distance ds = vsT  Wave crests are a distance λ´ = d - dsapart: Wavelength seen by observer: λ´ = λ - vsT = λ - (vs/v)λ = λ[1 - (vs/v)]  Frequency seen by observer: f´ = (v/λ´) = (v/λ)/[1 - (vs/v)] Or: f´ = f/[1 - (vs/v)] > f Observer hears a frequency higher than f

  8. In air, at rest, source frequency  f = 1/T, period T Speed of sound  v. Distance between crests: d = λ = vT . T = (λ/v) • Source movingAWAY FROM observer, speed vs • In time T =1/f, source moves a distance ds = vsT  Wave crests are a distance λ´ = d + dsapart:Wavelength seen by observer: λ´ = λ + vsT = λ + (vs/v)λ = λ[1 + (vs/v)] Frequency seen by observer:f´ = (v/λ´) = (v/ λ)/[1 + (vs/v)] Or: f´ = f/[1 + (vs/v)] < fObserver hears a frequency lower than f

  9. Stationary source, moving observer. Sound speed  v. Distance between crests: d = λ = vT, T = (λ/v), f = (v/ λ) Observer movesTOWARDS the source, speed vo. Relative velocity of source & observer: v´ = v + vo  Frequency seen by observer: f´ = (v´/λ) = (v + vo)/λ = (v + vo)(f/v) Or: f ´ = f[1 + (vo/v)] > f Observer hears a frequency higher than f

  10. Stationary source, moving observer. Sound speed v. Distance between crests: d = λ= vT, T = (λ/v), f = (v/ λ) Observer movesAWAY FROM source, speed vo Relative velocity of source & observer: v´ = v - vo  Frequency seen by observer: f´ = (v´/λ) = (v - vo)/λ = (v - vo)(f/v) Or: f ´ = f[1 - (vo/v)] < f Observer hears a frequency lower than f

  11. If BOTH observer AND source are moving. Observer velocity = vo . Source velocity = vs  Combine the two effects just discussed. f ´ = f[1  (vo/v)]/[1 -/+ (vs/v)] Top signs  Motion towards Bottom signs  Motion away from Example 12-14

  12. Example 12-15 • Sound reflected by a moving object. Need Doppler effect with BOTH observer AND source moving. • Initial wave: Object is “Observer” • Reflected wave: Object is “Source”

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