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 f 2 & f 1 ) alternately go through constructive & destructive interference. Beat Frequency  f B = f 2 - f 1

6. 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

7. Doppler Effect

9. 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 moving TOWARDS observer, speed  v s In time T =1/f, source moves a distance d s = v s T  Wave crests are a distance λ´ = d - d s apart: Wavelength seen by observer: λ´ = λ - v s T = λ - (v s /v)λ = λ[1 - (v s /v)]  Frequency seen by observer: f´ = (v/λ´) = (v/λ)/[1 - (v s /v)] Or: f´ = f/[1 - (v s /v)] > f Observer hears a frequency higher than f

10. 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 moving AWAY FROM observer, speed  v s In time T =1/f, source moves a distance d s = v s T  Wave crests are a distance λ´ = d + d s apart: Wavelength seen by observer: λ´ = λ + v s T = λ + (v s /v)λ = λ[1 + (v s /v)]  Frequency seen by observer: f´ = (v/λ´) = (v/ λ)/[1 + (v s /v)] Or: f´ = f/[1 + (v s /v)] < f Observer hears a frequency lower than f

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

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

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

14. 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”