speed of propagation

Examples of speed of propagation in the following topics:

• Transverse Waves

  • Transverse waves propagate through media with a speed $\vec{v}_w$ orthogonally to the direction of energy transfer.
  • When a wave travels through a medium--i.e., air, water, etc., or the standard reference medium (vacuum)--it does so at a given speed: this is called the speed of propagation.
  • The speed at which the wave propagates is denoted and can be found using the following formula:
  • where v is the speed of the wave, f is the frequency, and is the wavelength .
  • The direction of propagation of this wave is along the t axis.

• The Speed of Light

  • The speed of light in vacuum is a universal physical constant crucial to many areas of physics.
  • It is also the speed of gravity (i.e., of gravitational waves) predicted by current theories.
  • The first quantitative estimate of the speed of light was made in 1676 by Rømer.
  • The speed at which light waves propagate in vacuum is independent both of the motion of the wave source and of the inertial frame of reference of the observer.
  • Discuss the invariance of the speed of light and identify the value of that speed in vacuum

• A Physical Aside: Multipole Radiation

  • The propagation of electromagnetic waves from a source traveling slower and faster than the speed of light in the medium.

• Einstein's Postulates

  • Special relativity is based on Einstein's two postulates: the Principle of Relativity and the Principle of Invariant Light Speed.
  • The Principle of Invariant Light Speed: The speed of light c is a constant, independent of the relative motion of the source and observer.
  • Physicists assumed that there exists a stationary medium for the propagation of light, which they called "luminiferous aether. " In 1887, Michelson and Morley attempted to detect the relative motion of the Earth through the stationary luminiferous aether, but their negative results implied the speed of light c is independent of the motion of the source relative to the observer.
  • If you are on a train moving at a speed V and throw a ball in the direction of the train's movement, the baseball will travel at a speed v+V for an observer stationary on the ground.
  • What would be the speed of light from the laser pointer for a stationary observer on the ground?

• The Speed of Light

  • But what exactly is the speed of light?
  • It is just that: the speed of a photon or light particle.
  • The speed at which light propagates through transparent materials (air, glass, etc.,) is dependent on the refractive index of that material, n:
  • As mentioned earlier, the speed of light (usually of light in a vacuum) is used in many areas of physics.
  • Relate speed of light with the index of refraction of the medium

• Water Waves

  • Although we often observe water wave propagating in 2D , in this atom we will limit our discussion to 1D propagation.
  • As long as the waves propagate slower than the wind speed just above the waves, there is an energy transfer from the wind to the waves.
  • Although larger waves are more powerful, wave power is also determined by wave speed, wavelength, and water density.
  • In deep water, longer-period waves propagate faster and transport their energy faster.
  • We see a wave propagating in the direction of the phase velocity.

• Wavelength, Freqency in Relation to Speed

  • The frequency of a wave is the number of cycles per unit time -- one can think of it as the number of crests which pass a fixed point per unit time .
  • Frequency and wavelength can also be related-* with respects to a "speed" of a wave.
  • where v is called the wave speed, or more commonly,the phase velocity, the rate at which the phase of the wave propagates in space.
  • Finally, the group velocity of a wave is the velocity with which the overall shape of the waves' amplitudes — known as the modulation or envelope of the wave — propagates through space.
  • In , one may see that the overall shape (or "envelope") propagates to the right, while the phase velocity is negative.

• The Speed of a Wave on a String

  • The speed of a wave on a string can be found by multiplying the wavelength by the frequency or by dividing the wavelength by the period.
  • Find the speed of a wave on a string with the following properties: frequency:10 Hzwavelength:0.25 mSolution:$v=f\lambda\\ v=10 Hz* 0.25m\\ v=2.5 \frac ms$
  • A transverse wave is defined as a wave where the movement of the particles of the medium is perpendicular to the direction of the propagation of the wave.
  • In this case, the medium through which the waves propagate is the rope.
  • The speed of a wave on this kind of string is proportional to the square root of the tension in the string and inversely proportional to the square root of the linear density of the string:$v=\sqrt{\frac{T}{\mu}}$

• Huygens' Principle

  • Huygens's Principle states that every point on a wavefront is a source of wavelets, which spread forward at the same speed.
  • He was able to come up with an explanation of the linear and spherical wave propagation, and derive the laws of reflection and refraction (covered in previous atoms) using this principle.
  • where s is the distance, v is the propagation speed, and t is time.
  • Each point on the wavefront emits a wave at speed, v.
  • The direction of propagation is perpendicular to the wavefront, as shown by the downward-pointing arrows.

• Frequency of Sound Waves

  • Frequency is dependent on wavelength and the speed of sound.
  • Alternatively, you can use the frequency and the wavelength to find the speed of sound in a specific medium.
  • Remember that sound travels at different speeds in different mediums; sound moves fastest through a solid.
  • The following equation is used to find the specific speed of sound, and is often easier to use than the standard speed of sound equation: vs=f∗λv_s=f*\lambda
  • A sound wave emanates from a source vibrating at a frequency f, propagates at v, and has a wavelength λ.