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**Understanding**

➔ The Doppler effect for sound waves and light waves

**Applications and skills:**

• Sketching and interpreting the Doppler effect when there is relative motion between source and observer

• Describing situations where the Doppler effect can be utilized

• Solving problems involving the change in frequency or wavelength observed due to the Doppler effect to determine the velocity of the source/observer

**Data Booklet reference:**

• Moving source: *f* ‘ = *fv*/(*v* ± *u*s)

• Moving observer: *f* ‘ = *f*(*v* ± *u*o)*/v*

• ∆*f* / *f* = λ / ∆λ ≈ *v* / *c*

### 9.5 The Doppler Effect

#### Definition: “Doppler effect is the change in the observed frequency of a wave when there is relative movement when there is relative movement between the source and the observer.”

Wavefront diagrams

#### Cases

Quantities:

f = Frequency of the source;

f’ =Apparent frequency, heard by the observed;

v = Speed of the wave;

us = Velocity of the source;

uo = Velocity of the observer.

Moving source and stationary observer:

– us for a source moving towards a stationary observer. f’ > f, because λ are shorter, as the wavefronts are being compressed.

+ us for a source moving away from a stationary observer. f’ < f, because λ are longer.

v, as measured by the observer, is v, since it is determined by the medium’s properties.

Stationary source and moving observer:

λ remains equal and v changes, as the medium changed: source – air; observer – moving air.

– uo for an observer moving away from a stationary source. f’ < f, but measured λ is constant.

+ uo for an observer moving towards a stationary source. f’ > f, but measured λ is constant.

Examples

Police speed radar: car moving away, reflecting microwaves from the source.

Medical physics: blood flow measurement

The machine detects when that expected speed (from the beat frequency) varies, due to constriction or obstruction of the vessel.

### Doppler effect with light

Formula different for sound, as the velocity of light is constant in all inertial reference frames (by special relativity), which means that, when measured by an observed who is not accelerating, the observer will measure the speed of light to be 3 x 10^8 ms^-1.

Blue-shift: If the source of light approaches, then the frequency increases and the wavelength decreases.

Red-shift: If the source of light moves away, then the frequency decreases and the wavelength increases.

Expanding Universe proof: Light from distant galaxies measured on Earth shows a red-shift, what indicates galaxies are moving away from us, and thus, the universe is expanding.

### DOPPLER EFFECT

When a source of sound and an observer or both are in motion relative to each other there is an apparent change in frequency of sound as heard by the observer. This phenomenon is called the Doppler’s effect.Apparent change in frequency

- When source is in motion and observer at rest
- when source moving towards observer

- when source moving away from observer

Here V = velocity of soundVS = velocity of sourceν0 = source frequency.

- When source is at rest and observer in motion
- when observer moving towards source

- when observer moving away from source and

V0 = velocity of observer.

- when observer moving away from source and

- When source and observer both are in motion
- If source and observer both move away from each other.

- If source and observer both move towards each other.

When the wind blows in the direction of sound, then in all above formulae V is replaced by (V + W) where W is the velocity of wind. If the wind blows in the opposite direction to sound then V is replaced by (V – W).

KEEP IN MEMORY

- The motion of the listener causes change in number of waves received by the listener and this produces an apparent change in frequency.
- The motion of the source of sound causes change in wavelength of the sound waves, which produces apparent change in frequency.
- If a star goes away from the earth with velocity v, then the frequency of the light emitted from it changes from ν to ν’.

ν’ = ν (1–v/c), where c is the velocity of light and where is called Doppler’s shift.

If wavelength of the observed waves decreases then the object from which the waves are coming is moving towards the listener and vice versa.