Physics 11

Waves 6 – Doppler EffectWaves 6 – Doppler Effect

Constructive & Destructive Interference:

+ =

Const r uct ive int er f er ence

+ =

Dest r uct ive int er f er ence

cancellat ion

When waves meet: v v

v

v

M ee tin g w avesou t o f ph ase

M ee tin g w avesin o f ph ase

Standing Waves: 1

2

3

4

5

6

7

8

Tim e L a pse View o f S tan d in g W ave

Waves and Wave Length:

The standing wave to the The standing wave to the left represents one half of left represents one half of the wavelength of the the wavelength of the wave or ½ wave or ½ . .

This would be a complete This would be a complete wave cycle or 2/2 wave cycle or 2/2 or 1 or 1 ..

This would be 3/2 This would be 3/2 or 1 or 1 ½ wave.½ wave.

Fundamental Frequencies:

fu n d a m e n ta l fr e q u e n c y1 s t h a rm o n ic

2 n d h a rm o n ic

3 rd h a rm o n ic

Interference is a characteristic of all waves.

Standing Waves When two sets of waves of equal amplitude

and wavelength pass through each other in opposite directions, it is possible to create an interference pattern that looks like a wave that is “standing still.” It is a changing interference pattern.

Demo - Rope and strobeDemo - Rope and strobe Demo - Mechanical overhead modelDemo - Mechanical overhead model

Visible Spectrum:

θ

Sonic boom manifested by condensation of water in air

Sonic Boom:

sin = vsound/vsource = 1/“Mach number”

Sonic boom of bullet in flight(holographic interferometry?)

Sonic Boom:

How fast is the bullet traveling?How fast is the bullet traveling? Mach # = 1/sinMach # = 1/sin

Super Sonic Flight:

http://stokes.byu.edu/http://stokes.byu.edu/teaching_resources/teaching_resources/boom_script_flash.htmlboom_script_flash.html

DOPPLER EFFECT

Refers to the change in frequency when there is

relative motion between an observer of waves and

the source of the waves

Doppler Movie - Doppler Movie - URL

Doppler Movie - URLDoppler Movie - URL

When a source of waves and an observer of When a source of waves and an observer of waves are getting closer together, the observer waves are getting closer together, the observer of the waves “sees” a frequency for the waves of the waves “sees” a frequency for the waves that is higher than the emitted frequency.that is higher than the emitted frequency.

When a source of waves and an observer of When a source of waves and an observer of waves are getting farther apart, the observer waves are getting farther apart, the observer of the waves “sees” a frequency for the waves of the waves “sees” a frequency for the waves that is lower than the emitted frequency.that is lower than the emitted frequency.

All waves exhibit the Doppler effect.

A particularly interesting example is used by

astronomers to determine if light emitting objects

(such as stars) are getting closer to us or farther

away.

On average most stars are moving farther away,

and their light spectra are “red shifted.”

Red Shift: Moving Away from sourceRed Shift: Moving Away from source

Actual Visual SpectrumActual Visual Spectrum

Observed Visual SpectrumObserved Visual Spectrum

Blue Shift: Moving towards sourceBlue Shift: Moving towards source

Actual Visual SpectrumActual Visual Spectrum

Observed Visual SpectrumObserved Visual Spectrum

Radar bounced off a spinning planet can

exhibit a Doppler effect and lead to a

determination of the spin rate of the planet.

This was used to discover that Venus has a This was used to discover that Venus has a

retrograde spin.retrograde spin.

Of course police use the Doppler effect to Of course police use the Doppler effect to

catch speeding motorists.catch speeding motorists.

BOW WAVES

Waves in front of moving object pile up. The familiar bow wave generated by a speedboat

knifing through the water It is a non-periodic wave produced by the

overlapping of many periodic circular waves. It has a constant shape.

Video Demonstration:

Demo 2.1 – Waves & Wake from Phys123Demo 2.1 – Waves & Wake from Phys123

SHOCK WAVES

Just as circular waves move out from a swimming bug, spherical waves move out from a flying object. If the object flies faster than the waves, the result is a cone-shaped shock wave.

There are two booms, one from the front of the flying object and one from the back.

Video Demonstrations:

- slower than the speed of soundSubsonic

Supersonic - faster than the speed of sound

Mach Number = speed of sound

speed of object