# [Answer] What is the relationship among frequency wavelength and wave speed?

###### Answer: Wave speed is frequency multiplied by wavelength.
What is the relationship among frequency wavelength and wave speed?

Dispersion occurs when pure plane waves of different wavelengths have different propagation velocities so that a wave packet of mixed wavelengths tends to spread out in space. The speed of a plane wave is a function of the wave’s wavelength : = (). The wave’s speed wavelength and frequency f are related by the identity = ().The function () expresses the dispersion relation of the given …

In linear media any wave pattern can be described in terms of the independent propagation of sinusoidal components. The wavelength λ of a sinusoidal waveform traveling at constant speed v is given by $\lambda ={\frac {v}{f}}\ \$ where v is called the phase speed (magnitude of the phase velocity) of the wave and f is the wave’s frequency. In a dispersive medium the phase speed itself depends upon the frequency of the wave making the relationship between wavelength and frequency nonlinear.

In linear media any wave pattern can be described in terms of the independent propagation of sinusoidal components. The wavelength λ of a sinusoidal waveform traveling at constant speed v is given by $\lambda ={\frac {v}{f}}\ \$ where v is called the phase speed (magnitude of the phase velocity) of the wave and f is the wave’s frequency. In a dispersive medium the phase speed itself depends upon the frequency of the wave making the relationship between wavelength and frequency nonlinear. In the case of electromagnetic radiation—such as light—in free space the phase speed is the speed of light about 3×10 m/s. Thus the wavelength of a 100 MHz electromagnetic (radio) wave is about: 3×10 m/s divided by 10 Hz = 3 metres. The wavelength of visible light ranges from deep red roughly 700 nm to violet roughly 400 nm (for other examples see electromagnetic spectrum). For sound waves in air the speed of sound is 343 m/s (at room temperature and atmospheric pressure). The wavelengths of sound frequencies audible to the human ear (20 Hz–20 kHz) are thus between approximately 17 m and 17 mm respectively. Somewhat higher frequencies are used by bats so they can resolve targets smaller than 17 mm. Wavelengths in audible sound are much longer than those in visible light. A standing wave is an undulatory motion that stays in one place. A sinusoidal standing wave includes stationary points of no motion called nodes and the wavelength is twice the distance between nodes. The upper figure shows three standing waves in a box. The walls of the box are considered to require the wave to have nodes at the walls of the box (an example of boundary conditions) determining which wavelengths are allowed. For example for an electromagnetic wave if the box has ideal metal walls th…

Dispersion relation – Wikipedia

Wavelength – Wikipedia

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Wavelength – Wikipedia

In linear media any wave pattern can be described in terms of the independent propagation of sinusoidal components. The wavelength λ of a sinusoidal waveform traveling at constant speed v is given by $\lambda ={\frac {v}{f}}\ \$ where v is called the phase speed (magnitude of the phase velocity) of the wave and f is the wave’s frequency. In a dispersive medium the phase speed itself depends upon the frequency of the wave making the relationship between wavelength and frequency nonlinear.

In linear media any wave pattern can be described in terms of the independent propagation of sinusoidal components. The wavelength λ of a sinusoidal waveform traveling at constant speed v is given by $\lambda ={\frac {v}{f}}\ \$ where v is called the phase speed (magnitude of the phase velocity) of the wave and f is the wave’s frequency. In a dispersive medium the phase spee…