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.

• 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!

• As a function of time, the two interfering waves (frequencies f2 & f1) alternately go through constructive & destructive interference.

• Beat Frequency fB = f2 - f1

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

Doppler Effect

• 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 vs

• In time T =1/f, source moves a distance ds = vsT Wave crests are a distance λ´ = d - ds apart:

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

• 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 vs

• In time T =1/f, source moves a distance ds = vsT Wave crests are a distance λ´ = d + ds apart: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

• 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 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

• 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 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

• 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

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”