Today’s Topic:

The Doppler Effect

Learning Goal:

SWBAT explain what the Doppler Effect is

and why it occurs.

A person operating a wave generator

finds that when she sets the function

generator to 116 Hz, she sees a string

with 5 nodes.

What frequency corresponds to the 7th

harmonic?

HomeworkDue Tuesday, 6/9:

Complete the Wave Interference

Worksheet

Two Days Late:

Complete the Wave Speed Worksheet

Movement of WavesWe are going to watch two very short

clips.

I want you to compare the sound of the

train horn as it passes us by and the

sound of the racecar as it passes us by.

What do these objects have in common?

What are we hearing?

Weeee-oooooWhat we’re hearing is something known

as the Doppler Effect.

The apparent change in frequency due

to the motion of the source of the sound

is called the Doppler Effect.

If you, the receiver of the frequency, also

move – you can also experience the

Doppler Effect.

But let’s back up for a minute.

The Doppler EffectWhile this effect happens with all types of

waves, it’s easiest to talk about the

Doppler Effect when we discuss sound.

But because it’s impossible to see sound

waves, we’re going to need to create an

analogy of what’s happening.

Let’s imagine there’s a small bug

standing in the middle of a puddle, but it

is vibrating up and down, creating ripples

in the puddle.

The Doppler EffectIf the bug vibrates up and down with a

constant frequency, the waves are going

to produce concentric circles, like in this

figure:

The waves will reach points A and B at

the same time, with the same frequency.

The Doppler EffectNow imagine that the bug now travels to

point B slower than the wave travels.

The waves no longer appear as

concentric circles. The centers of the

circles now move in the direction of the

swimming bug.

The Doppler EffectAs a result, an observer at B would

encounter wave crests more often.

More waves

per second…

The observer at B encounters a higher

frequency. This again, is because the bug is

moving towards B, so B sees the waves more

frequently than if the bug were not moving.

The waves don’t travel as far.

There’s a term

for that…

The Doppler EffectAn observer at A, on the other hand,

encounters the wave at a lower

frequency.

The waves take a longer time to get to A,

as there is more of a distance the waves

need to travel to get to A.

The Doppler EffectAs a wave source moves towards an

observer, the observer encounters waves

with a higher frequency.

As the wave moves away from an

observer, the observer encounters waves

with a lower frequency.

The Doppler EffectWater waves travel across the surface of

water, but sound waves travel like a

sphere.

The Doppler effect is very noticeable

when you hear a train passing by, a car

horn, police siren, or an ambulance.

The Doppler EffectOddly enough, the Doppler effect also

occurs in light too.

When a light source approaches an

observer, there is an in the

perceived frequency.

When a light source travels away from

an observer, there is a in the

perceived frequency.

increase

decrease

The Doppler Effect

An increase in frequency is called a blue

shift, because the increase is towards

the high-frequency, or blue, end of the

spectrum.

The Doppler Effect

A decrease in frequency is called a red

shift, referring to the low-frequency, or

red, end of the spectrum.

The Doppler EffectDistant galaxies show a red shift when

they are observed.

What does that mean about the motion of

these galaxies relative to Earth?

Looking at that color, astronomers are

able to determine how quickly they’re

traveling from Earth.

The Doppler EffectRapidly spinning stars will show both a

blue shift and red shift. A blue shift will

appear on half of the planet, while the red

shift will occur on the other half.

This information tells astronomers how

fast a star is spinning.

This video explains it a bit more.

Physics Fun Fact: Radar Guns

Police officers utilize the Doppler effect in

their cars to catch speeders.

Radar guns emit microwaves towards a

moving car, which then bounce back.

The reflections are received by the gun,

and the speeder’s speed is calculated.

Doppler Effect FormulaWe have a formula that mathematically

explains what our ears and eyes

perceive.

The formula depends on your situation:

Doppler Effect FormulaIf neither your wave source or observer is

moving, will the Doppler Effect be

observed?

No.

If neither the source nor the observer are

moving, there is no change in the

apparent frequency.

Doppler Effect FormulaIf the wave source is moving towards an

observer at rest:

f ’= 𝑣

(𝑣 − 𝑣𝑠)

fWhere:

v = velocity of sound or light in medium

vs = velocity of the source

f = real frequency

f’ = apparent frequency

Doppler Effect FormulaIf the wave source is moving away from

an observer at rest:

f ’= 𝑣

(𝑣 + 𝑣𝑠)

fWhere:

v = velocity of sound or light in medium

vs = velocity of the source

f = real frequency

f’ = apparent frequency

Doppler Effect FormulaIf the observer is moving towards a

stationary wave source:

f ’= (𝑣 + 𝑣

𝑜)

𝑣f

Where:v = velocity of sound or light in medium

vo = velocity of the observer

f = real frequency

f’ = apparent frequency

Doppler Effect FormulaIf the observer is moving away from a

stationary wave source:

f ’= (𝑣 − 𝑣

𝑜)

𝑣f

Where:v = velocity of sound or light in medium

vo = velocity of the observer

f = real frequency

f’ = apparent frequency

Doppler Effect FormulaThis formula can be combined to the

following combination:

f ’= (𝑣 ± 𝑣

𝑜)

(𝑣 ∓ 𝑣𝑠)

fWhere:

v = velocity of sound or light in medium

vs = velocity of the source

vo = velocity of the observer

f = real frequency

f’ = apparent frequency

Sample ProblemsOn a 16 ⁰C day, a police car produces a

siren with a frequency of 1200 Hz while

traveling at 30 m/s towards a stationary

passerby.

What is the apparent frequency

experienced by the observer?

What frequency do they hear as the car

drives away?

Sample ProblemsOn a stormy 24 ⁰C day in Indiana, a

tornado siren emits an alarm at 2500 Hz.

What frequency does someone hear

while they stand up (not moving) to leave

their house?

What frequency does the driver hear as

they drive away from the siren at a rate of

8 m/s?