Grade 11
  1. Mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two and three dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration and deceleration  1.1.6. Graphical analysis of motion  1.1.7. Equations of motion (advanced derivations)  1.1.8. Free fall and terminal velocity  1.1.9. Projectile motion  1.1.10. Relative velocity in one and two dimensions  1.1.11. Motion of a car on an inclined plane  1.2. Dynamics  1.2.1. Newton's laws of motion and their applications  1.2.2. Inertia and Newton's first law  1.2.3. Force and types of force  1.2.4. Static and kinetic friction  1.2.5. Circular motion and centripetal acceleration  1.2.6. Non-uniform circular motion  1.2.7. Banking of roads and curves  1.2.8. Momentum and Impulse  1.2.9. Conservation of momentum in one and two dimensions  1.2.10. Applications of Newton's Third Law  1.3. Work, Energy and Power  1.3.1. Work done by a constant and variable force  1.3.2. Work–energy theorem  1.3.3. Kinetic and potential energy  1.3.4. Gravitational and elastic potential energy  1.3.5. Conservation of mechanical energy  1.3.6. Power and instantaneous power  1.3.7. Efficiency of machines  1.3.8. Work done by conservative and non-conservative forces  1.4. Rotational motion  1.4.1. Torque and angular acceleration  1.4.2. Rotational equilibrium  1.4.3. Moment of inertia and its applications  1.4.4. Angular momentum and its conservation  1.4.5. Kinetic energy of rolling motion and rotation  1.4.6. Parallel and Perpendicular Axis Theorem  1.4.7. Dynamics of rotational motion
  2. Gravitational force  2.1. Universal gravitation  2.1.1. Newton's law of universal gravitation  2.1.2. Gravitational field and potential  2.1.3. Change in acceleration due to gravity  2.1.4. Kepler's laws of planetary motion  2.1.5. Orbital mechanics and satellites  2.1.6. Escape velocity and orbital velocity  2.1.7. Weightlessness and free fall  2.1.8. Gravitational potential energy and energy in orbits  2.1.9. Black holes and gravitational lensing
  3. Properties of matter  3.1. Fluid mechanics  3.1.1. Density and pressure in liquids  3.1.2. Pascal's theory and applications  3.1.3. Archimedes' Principle and Buoyancy  3.1.4. Bernoulli's equation and applications  3.1.5. Continuity equation and the Venturi effect  3.1.6. Surface tension and capillarity  3.1.7. Viscosity and Poiseuille's Law  3.1.8. Reynolds number and turbulence  3.2. Elasticity and deformation  3.2.1. Hooke's law and the stress-strain relation  3.2.2. Elastic modulus and applications  3.2.3. Deformation and yield strength of solids
  4. Thermal physics  4.1. Heat and temperature  4.1.1. Thermometric properties and temperature scale  4.1.2. Thermal expansion of solids, liquids and gases  4.1.3. Heat transfer system  4.1.4. Specific heat capacity and calorimetry  4.1.5. Latent heat and phase change  4.2. Kinetic theory of gases  4.2.1. Molecular model of gases  4.2.2. Kinetic explanation of temperature  4.2.3. Ideal Gas Equation and Deviations  4.2.4. Mean free path and Maxwell–Boltzmann distribution  4.3. Laws of Thermodynamics  4.3.1. Zeroth Law and Thermal Equilibrium  4.3.2. First Law and Internal Energy  4.3.3. The Second Law and Entropy  4.3.4. Carnot cycle and heat engines  4.3.5. Refrigerators and heat pumps
  5. Waves and oscillations  5.1. Simple Harmonic Motion  5.1.1. Equations of SHM  5.1.2. Energy in SHM  5.1.3. Damped and forced oscillations  5.1.4. Resonance and applications  5.1.5. Pendulum and spring-mass system  5.2. Wave motion  5.2.1. Types of mechanical waves  5.2.2. Wave motion and energy transport  5.2.3. Superposition Principle and Standing Waves  5.2.4. Reflection, Refraction and Diffraction  5.2.5. Doppler effect in sound and light  5.2.6. Pulsations and interference
  6. Electricity and Magnetism  6.1. Electrostatics  6.1.1. Electric charge and conservation  6.1.2. Coulomb's law and its applications  6.1.3. Electric field and electric flux  6.1.4. Electric potential and potential energy  6.1.5. Capacitance and Energy Stored in a Capacitor  6.2. Current Electricity  6.2.1. Ohm's law and electrical resistance  6.2.2. Resistivity and temperature dependence  6.2.3. Kirchhoff's Laws and Circuit Analysis  6.2.4. Electrical power and efficiency  6.2.5. Combination of resistors  6.3. Magnetism and Electromagnetism  6.3.1. Magnetic fields and their sources  6.3.2. Magnetic force on moving charges  6.3.3. Electromagnetic induction  6.3.4. Faraday's and Lenz's laws  6.3.5. Inductance and Transformer  6.3.6. Alternating current and its applications
  7. Optics  7.1. Reflection and Refraction  7.1.1. laws of reflection and refraction  7.1.2. Mirrors and lenses  7.1.3. Total internal reflection and optical fiber  7.2. Wave optics  7.2.1. Interference and Diffraction  7.2.2. Young's double-slit experiment  7.2.3. Polarization of light
  8. Modern Physics  8.1.1. Photoelectric effect and Einstein's theory  8.1.2. Wave–particle duality  8.1.3. Heisenberg's uncertainty principle  8.1.4. Compton Effect  8.2. Atomic and Nuclear Physics  8.2.1. Atomic model and energy levels  8.2.2. Radioactive decay and half-life  8.2.3. Nuclear Fission and Fusion
  9. Electronics and Communication  9.1. Semiconductors  9.1.1. pn junction and diode  9.1.2. Transistors and Logic Gates  9.1.3. Integrated Circuits and Applications  9.2. Communication Systems  9.2.1. Basics of Analog and Digital Communication  9.2.2. Wireless and Optical Communication  9.2.3. Modulation and Demodulation

Grade 11 → Waves and oscillations → Wave motion ↓


Doppler effect in sound and light


The Doppler effect, named after Austrian physicist Christian Doppler, is a fascinating phenomenon in the world of waves. It describes the changes in the frequency or wavelength of a wave relative to an observer moving relative to the wave source. This effect is most commonly associated with sound waves, but it applies to light waves as well as other types of waves. Understanding the Doppler effect is important in explaining a variety of real-world phenomena, from the pitch of a passing siren to the redshift observed in distant galaxies.

Understanding wave motion

Waves are disturbances that transfer energy from one point to another without actual movement of the particles of the medium. Waves can be classified into two main types: mechanical waves, which need a medium to travel (such as sound waves), and electromagnetic waves, which can travel through a vacuum (such as light waves).

The following terms are essential in wave motion:

  • Frequency ((f)): The number of wave cycles passing a point per unit time, measured in hertz (Hz).
  • Wavelength ((lambda)): The distance between two successive crests or troughs of a wave.
  • Velocity ((v)): The speed at which the wave travels through the medium.

Doppler effect in sound

When we think about the Doppler effect, we often start with sound waves. Imagine you are standing on the side of the road and a car with a siren approaches you, passes you, and then drives away. As the car approaches you, the siren seems louder than as the car moves away. This change in sound is caused by the Doppler effect.

The formula to calculate the observed frequency ((f')) due to Doppler effect for sound is given by:

f' = left(frac{v + v_o}{v + v_s}right) cdot f

Where:

  • f is the actual frequency of the wave source.
  • v is the speed of sound in the medium.
  • v_o is the speed of the observer relative to the medium.
  • v_s is the speed of the source relative to the medium.

If the observer is moving towards the source, (v_o) is positive; if away, it is negative. Similarly, if the source is moving towards the observer, (v_s) is positive; if away, it is negative.

Text example

Let us take an example to illustrate the Doppler effect in sound. Suppose a police car with a siren emitting sound at a frequency of 700 Hz is moving towards a stationary observer at a speed of 20 m/s. If the speed of sound in air is 340 m/s, what frequency does the observer hear? 

f' = left(frac{340}{340 - 20}right) cdot 700

Simplification,

f' = left(frac{340}{320}right) cdot 700 = left(frac{17}{16}right) cdot 700 = 743.75, text{Hz}

The observer hears a sound at about 744 Hz, higher than the original 700 Hz, because the sound waves are compressed as the sound source moves toward the observer.

Visual example

Consider this scenario visually:

car with siren supervisor

In the visual illustration, the car is emitting sound waves represented by the blue lines. As the car moves toward the observer, these waves are compressed, resulting in a higher frequency for the observer.

Doppler effect in light

The Doppler effect also applies to light, although it is somewhat different due to the nature of electromagnetic waves. In the field of light, the Doppler effect manifests as a shift in the wavelength and frequency of light. When an object emitting light moves toward an observer, the light appears to shift toward the blue end of the spectrum, known as a blueshift. Conversely, when the object is moving away, the light appears to shift toward the red end, known as a redshift.

The formula for observed frequency ((f')) for light waves is:

f' = left(frac{c + v_o}{c + v_s}right) cdot f

Where:

  • f is the actual frequency of the light source.
  • c is the speed of light in vacuum, approximately (3 times 10^8) m/second.
  • v_o is the velocity of the observer.
  • v_s is the velocity of the source.

Text example

Imagine that a star emits light at a frequency of (6 times 10^{14}) Hz, and it is moving away from the Earth at a speed of (1 times 10^6) m/s. What is the observed frequency of the light on Earth? 

f' = left(frac{3 times 10^8}{3 times 10^8 + 1 times 10^6}right) cdot (6 times 10^{14})

Simplification,

f' = left(frac{3 times 10^8}{3.01 times 10^8}right) cdot (6 times 10^{14})

Just calculate the slight decrease in frequency as the star moves away.

Visual example

Visual depiction of a star moving away:

star Earth

In the view, the red dashed line shows light waves that stretch out as the star moves away from Earth, causing redshift.

Applications of Doppler effect

The Doppler effect has applications in many areas:

  • Astronomy: Redshift and blueshift help astronomers determine the speed of stars and galaxies, which is helpful in the expanding universe theory.
  • Weather radar: Doppler radar uses variations in the frequency of returned radar waves to measure wind speed in weather systems.
  • Medical imaging: Doppler ultrasound helps monitor blood flow in medical diagnosis.
  • Speed detection: Police use the Doppler effect in radar guns to measure the speed of moving vehicles.

Conclusion

The Doppler Effect is an important concept in understanding wave behavior when the source or observer is in motion. Whether it's hearing a change in the sound of a siren or seeing a color change in light from distant galaxies, the Doppler Effect provides valuable insight. Through the exploration of both sound and light, we are able to understand the versatility and importance of this phenomenon in scientific and practical applications around the world.


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Doppler effect in sound and light

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