• Waves: Revision
• The Doppler Effect
• Applications of the Doppler Effect with ultrasound waves
• Applications of the Doppler Effect with light

5.1 Waves: Revision

Vibrations cause waves and waves cause vibrations.
There are two kinds of waves: transverse waves and longitudinal waves.

Transverse waves The disturbance of the medium is perpendicular to the direction in which the wave is propagated (transmitted). Examples: water waves, electromagnetic waves (light, radio waves, X-rays etc.)

Longitudinal waves The disturbance of the medium is parallel to the direction of propagation of the pulse. Example: sound waves, slinky spring

5.1.1 Wave properties

• The amplitude (height) of a wave motion is the maximum displacement of the particles from their equilibrium (rest) position.
  The amplitude determines the volume of a sound wave.
• The wavelength (λ) of a wave is the distance between two consecutive points in the wave which are in phase and is measured in metres (m).
  It is therefore also the distance between two successive crests or the distance between two successive troughs.
• The frequency (f) of a wave motion is the number of complete waves passing a specific point per second and is measured in hertz (Hz).
  The frequency of a sound wave determines its pitch. The frequency of a light wave determines its colour.
• The frequency of a wave determines the energy of the wave.
• The higher the frequency, the higher the energy. So E ∝ f

The period (T) of a wave motion is the time taken for one complete wave to pass a fixed point. f = number of waves passing a point                             time and       T =              time                     number of waves passing a point The speed (v) of a wave is the rate at which the energy is propagated by the wave and is measured in m⋅s−1. v = f λ where v is speed (m·s–1) f is frequency (Hz) λ is wavelength (m) T = 1         f and f = 1       T T is the period of the graph (s) f is the frequency (Hz)

5.1.2 Light

• The visible spectrum of light is just a small section of a much greater series of wavelengths called the electromagnetic spectrum.
• The speed of light (and all other electromagnetic radiation) is constant (3 × 108 m·s⁻¹).
• The colour of light depends on its frequency.
• In the colour spectrum, red has the longest wavelength and lowest frequency and violet has the shortest wavelength and the highest frequency.

The Visible Light Spectrum

For light: c = f λ
c is the speed of an
electromagnetic wave (m·s–1)
c = 3 × 108 m·s−1
f is frequency (Hz)
λ is wavelength (m)

5.2 The Doppler Effect

The Doppler Effect is the change in frequency or pitch of the sound or the colour of light that is detected when the wave source and the observer move relative to each other.
Vocabulary: Frequency means “how often”. “Observer” means person who sees, hears, or otherwise comes to know through the senses.

Example
When a car approaches a listener:

• the sound waves emitted by the car’s hooter are compressed in front of the car;
• more sound waves reach the listener per second and
• the pitch appears to be higher than the sound emitted by the source (the car’s hooter). The opposite is true when the car moves away from the listener.

Activity 1

1. A sound source approaches a stationary (not moving) observer at constant velocity. Which ONE of the following describes how the observed frequency and wavelength differ from that of the sound source?

   Observed Wavelength	Observed Frequency
   A. Greater than	Greater than
   B. Less than	Less than
   C. Greater than	Less than
   D. Less than	Greater than

   1. Greater than
   2. Less than
   3. Greater than Less than
   4. Less than Greater than (2)
2. Which one of the following is the main principle applied when using the rate of blood flow or the heartbeat of a foetus in the womb?
   
   1. Doppler Effect.
   2. Photoelectric effect
   3. Huygens principle
   4. Diffraction (2)
3. An ambulance approaches an accident scene at constant velocity.
   The siren of the ambulance emits sound waves at a frequency of 980 Hz. A detector at the scene measures the frequency of the emitted sound waves as 1 050 Hz.
   
   1. Calculate the speed at which the ambulance approaches the accident scene. Use the speed of sound in air as 340 m·s^–1 (6)
   2. Explain why the measured frequency is higher than the frequency of the source. (2)
   3. The principle of the Doppler Effect is applied in the Doppler flow meter. State ONE positive impact of the use of the Doppler flow meter on humans. (2)
4. The siren of a stationary (not moving) ambulance emits sound waves at a frequency of 850 Hz.
   An observer (person witnessing this) who is travelling in a car at a constant speed in a straight line, begins measuring the frequency of the sound waves emitted by the siren when he is at a distance x from the ambulance. The observer continues measuring the frequency as he approaches, passes, and moves away from the ambulance. The results obtained are shown in the graph below.
   
   
   1. The observed frequency suddenly changes at t = 6s. Give a reason for this sudden change in frequency. (1)
   2. Calculate
      b(1) The speed of the car (Take the speed of sound in air as 340 m·s–1) (5)
      b(2) Distance x between the car and the ambulance when the observer BEGINS measuring the frequency. (3)
      [23]

Solutions D (2) A (2) fL = V ± VL (fs) OR fL = V (fs)           V ± VL                (V – Vs) ∴ 1050 3 – (340 – 0) / (340 – Vs) × 980 ∴ Vs = 22,67 m/s (6) Waves in front of the moving source are compressed. The observed wavelength decreases (3). For the same speed of sound (3), a higher frequency will be observed. (2) Determine whether arteries are clogged or narrowed (3), so that precautions can be taken to prevent heart attack or stroke (3), OR Determine the heartbeat (3) of a foetus to assure that the child is alive or does not have a heart defect (3). (2) The approaching observer (higher f) passes the source at t = 6 s and moves away (lower f) from the source. (3) (1) (1) Option 1. Approaching observer: fL = V ± VL (fs)           V ± Vs OR fL = V + VL (fs)             V ∴ 900 3 = (340 + VL) (850) / (340) ∴ VL = 20 m/s (5) Option 2. Observer moving away: fL = V ± VL (fs)           V ± Vs OR fL = V - VL (fs)             V ∴ 800 = (340 – VL) (850) / (340) ∴ VL = 20 m/s (5) Notes: any other correct Doppler Effect formula gets maximum 3/4 marks. (2) Option 1. Δx = v1Δt + ½ aΔt2 = (20)(6) + ½ (0)Δt2 = 120 m Option 2. Δx = vΔt = (20)(6) = 120 m (3) Note: accept s = ut or s = vt, as well as s = ut + ½at2, as well as Δy = v1Δt + ½aΔt2 [23]

Activity 2
An ambulance moving at 40 m·s^–1 approaches a traffic light where a blind man and his dog wait to cross a road. The siren of the ambulance (source) emits sound waves at a frequency of 350 Hz (fs). The pitch of the sound that the man hears increases as the ambulance moves towards him and decreases as the ambulance passes him and moves away.

1. If the speed of sound in air is 340 m·s^–1, determine the frequency (fL) of the sound waves that the man hears while the ambulance approaches him. (3)
2. Explain how this effect can help a blind person waiting to cross the road. (2)
   [5] 

Solutions fL =   (V±VL)            (V±VS)fS fL =         (340+0)                  (340 - 40) x 350Hz fL = 396,67 Hz (3) When crossing a street, a blind person can determine whether a car is moving towards or away from him. If the pitch of a vehicle decreases, the person knows that the vehicle is moving away from him, and vice versa. (2) [5]

5.3 Applications of the Doppler Effect with ultrasound waves

The Doppler flow meter is used to measure the rate of blood flow in a patient’s blood vessels.

• Ultrasound is a longitudinal wave with very high frequency of above 20 kHz that we cannot hear.
• A catheter connected to a Doppler flow meter is inserted in a blood vessel. It gives out a sound wave at ultrasound frequency. The blood velocity through the heart causes a ‘Doppler shift’ in the frequency of the returning waves. The meter measures this and compares the frequencies.
• The receiver detects the reflected sound and an electronic counter measures the reflected frequency.
• From the change in frequency, the speed of the blood flow can be determined and narrowing of blood vessels identified.

5.4 Applications of the Doppler Effect with Light

The electromagnetic Spectrum
The electromagnetic spectrum is the full range of types of electromagnetic radiation.
Electromagnetic radiation consists of waves which have both an electric and magnetic component. They are transverse waves. They are emitted by many objects eg. the sun, lights, fires, stoves, persons.
All forms of light, radio, and heat at a distance, are electromagnetic radiation. Note that electromagnetic radiation is NOT the same as radioactivity except for gamma waves, which come from nuclear reactions.
The electromagnetic spectrum is shown on the next page.
Visible light is part of the electromagnetic spectrum.

• Stars, like the sun, emit light.
• When a star moves away from the Earth, its spectrum shifts to longer wavelengths (lower frequencies) – in other words, the red side of the spectrum. The star appears red.
• When a star moves towards the Earth, its spectrum shifts to shorter wavelengths (higher frequencies) – in other words, the blue side of the spectrum. The star appears blue.

Remember:
The wavelength of light is usually measured in nm (nanometers) and must be converted to m (metres) before doing any calculations. 1 nm = 1 × 10^–9 m

Ultrasound machines use the Doppler Effect to get readings of unborn babies in the womb so that doctors can see if the baby is healthy.