Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Classical mechanics → Oscillations and waves ↓


Sound Waves and the Doppler Effect


Introduction

Sound waves are a fascinating part of physics, representing mechanical waves that travel through a medium, especially through air. They are generated due to vibrations and carry energy from one place to another. Sound is important in our daily lives, enabling communication and enriching various experiences from music to alert systems. When combined with the Doppler effect, sound waves reveal a realm of interesting phenomena that we can observe and use in various applications.

What are sound waves?

Sound waves are longitudinal waves produced by vibrating objects. They need a medium such as air, water, or solids to travel. These vibrations cause particles in the medium to oscillate parallel to the direction of the wave, creating regions of compression and rarefaction, which are periods when the air is compressed and expanded:

          -----> Compressed Air Particles 
          <----- air particles spread

The frequency of sound waves determines the pitch, while the amplitude determines the volume. Sound waves can travel at different speeds depending on the medium, with sound generally traveling much faster in solids than in liquids and gases.

Sound wave equation

A sound wave can be expressed mathematically using the wave equation:

            P(x,t) = P₀ sin(kx – ωt + φ)

Where:

  • p(x,t) is the pressure change at position x and time t.
  • P₀ is the maximum pressure change (amplitude).
  • k is the wavenumber, which is equal to 2π/λ (where λ is the wavelength).
  • ω is the angular frequency, 2πf (where f is the frequency).
  • φ is the phase of the wave.

Doppler effect

The Doppler effect, named after Austrian physicist Christian Doppler, is a noticeable change in the frequency or wavelength of a wave relative to an observer moving relative to the wave source. For sound waves, it is observed whenever there is relative motion between the sound source and the observer. This effect is the reason why an ambulance siren seems to change pitch as it passes you.

Understanding the Doppler Effect with a simple example

Imagine you are standing on the roadside and a car is moving towards you blowing its horn. As it comes closer to you, the sound of the horn gets louder because the sound waves get compressed. As the car moves further and further away, the sound of the horn gets lower because the sound waves get stretched.

The change in frequency reflects the Doppler effect and can be expressed mathematically. For a sound wave, assuming the source is moving toward a stationary observer:

            f' = f (v + v₀) / (v - v₀)

Where:

  • f' is the observed frequency.
  • f is the source frequency.
  • v is the speed of sound in the medium.
  • v₀ is the velocity of the observer.
  • vs is the velocity of the source.

Visual example

Sound wave propagation

direction of sound wave

Notice how sound waves propagate as the particles in the medium vibrate about their equilibrium positions.

Example of the Doppler Effect in action

car approaching sound waves are compressed receding sound waves spread out

This illustration shows a car moving to the right, with compressed sound waves (high frequency, high pitch) on the left and spread out sound waves (low frequency, low pitch) on the right.

Practical applications

The implications of understanding sound waves and the Doppler effect extend to a variety of real-world applications. Here are some of the areas where they find significant utility:

Medical imaging

One of its major applications is in medical diagnosis, particularly Doppler ultrasonography, which measures blood flow velocity. The principle of the Doppler effect allows technicians to determine the speed and direction of blood flow in vessels, which is useful for diagnosing a variety of conditions.

Astronomy

Astronomers use the Doppler effect to determine the speed of stars and galaxies. By looking at the shift in light frequency, astronomers can infer whether celestial objects are moving toward or away from Earth, which helps us understand the expansion of the universe.

Police and radar technology

Law enforcement agencies use radar guns that use the Doppler effect to measure the speed of vehicles. The frequency of the returned radar wave compared to the transmitted wave indicates the speed of the vehicle, helping in traffic monitoring and control.

Conclusion

The study of sound waves and the Doppler effect is an important chapter in the exploration of classical mechanics, linking practical applications and fundamental physics. The principles elucidated by these concepts enrich our understanding of wave dynamics and interactions. Understanding their role in the mechanics of everyday phenomena leads to deep insights and innovations in both technological and scientific fields.


Undergraduate → 1.8.5


U
username
0%
completed in Undergraduate

← Prev (1.8.4)
Wave properties and types
Next (1.8.6) →
Wave interference and superposition

Comments 



Sound Waves and the Doppler Effect

https://www.physicsflow.com/ug/1.8.5?pfal=en