The relationship between ω and λ (or k) is called a dispersion relation. In which wavelength and wavenumber are related to velocity and frequency as:ĭispersion causes separation of colors when light is refracted by a prism. They are also commonly expressed in terms of (radian) wavenumber k ( times the reciprocal of wavelength) and angular frequency ω ( times the frequency) as:
Where y is the value of the wave at any position x and time t, and A is the amplitude of the wave. Traveling sinusoidal waves are often represented mathematically in terms of their velocity v (in the x direction), frequency f and wavelength λ as: The wavelength, period, and wave velocity are related as before, if the stationary wave is viewed as the sum of two traveling sinusoidal waves of oppositely directed velocities. A sinusoidal standing wave includes stationary points of no motion, called nodes, and the wavelength is twice the distance between nodes. For example, when light enters another medium, its speed and wavelength change while its frequency does not this change of wavelength causes refraction, or a change in propagation direction of waves that encounter the interface between media at an angle.Ī standing wave (black) depicted as the sum of two propagating waves traveling in opposite directions (red and blue).Ī standing wave is an undulatory motion that stays in one place. The wavelengths of sound frequencies audible to the human ear (20 Hz–20 kHz) are between approximately 17 m and 17 mm, respectively, assuming a typical speed of sound of about 343 m/s the wavelengths in audible sound are much longer than those in visible light.įrequency and wavelength can change independently, but only when the speed of the wave changes. Visible light ranges from deep red, roughly 700 nm, to violet, roughly 400 nm (430–750 THz) (for other examples, see m). As an example, the wavelength of a 100 MHz electromagnetic (radio) wave is about: 3×10 8 m/s divided by 100×10 6 Hz = 3 metres. For sound waves in air, the speed of sound is 343 m/s (1238 km/h) (at room temperature and atmospheric pressure). In the case of electromagnetic radiation such as light in free space, the speed is the light, about 3×10 8 m/s. Where v is called the phase speed (magnitude of the phase velocity) of the wave and f is the wave's frequency. Refraction: when a plane wave encounters a medium in which it has a slower speed, the wavelength decreases, and the direction adjusts accordingly. For example, in waves over deep water a particle in the water moves in a circle of the same diameter as the wave height, unrelated to wavelength. Wavelength is a measure of the distance between repetitions of a shape feature such as peaks, valleys, or zero-crossings, not a measure of how far any given particle moves. In a crystal lattice vibration, atomic positions vary periodically in both lattice position and time. Water waves are periodic variations in the height of a body of water. A sound wave is a periodic variation in air pressure, while in light and other electromagnetic radiation the strength of the electric and the magnetic field vary. Įxamples of wave-like phenomena are sound waves, light, and water waves. Īssuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to frequency: waves with higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths. The term wavelength is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids. The concept can also be applied to periodic waves of non-sinusoidal shape. Wavelength is commonly designated by the Greek letter lambda (λ). It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. In physics, the wavelength of a sinusoidal wave is the spatial period of the wave – the distance over which the wave's shape repeats.
Wavelength of a sine wave, λ, can be measured between any two points with the same phase, such as between crests, or troughs, or corresponding zero crossings as shown.