A wave is a disturbance moving through a medium. The medium can be air, liquid, or solid. The wave travels through the medium and carries energy with it.

The wavelength of a wave is the distance between two crests (highest point) of consecutive waves. Its unit is metre (m).

The amplitude of a wave is a measure of the intensity of the energy the wave carries. For example, a note played on a musical instrument may be played louder (greater amplitude) without changing the pitch (frequency), wavelength, or velocity (sound in air is a constant 340 m/s).

The frequency of a wave is equal to the wave's velocity divided by its wavelength. As the wavelength increases, the frequency decreases. Frequency is a measure of the number of waves (crest to crest) passing a point in space per second. It has the unit of hertz (Hz), which means 'per second'.

v = *f* . λ

The wavelength of a transverse wave is the distance between two consecutive crests of the wave. Its unit is metre (m).

Wavelengths of electromagnetic radiation can be any length, from nanometres to thousands or even millions of kilometres long.

As the wavelength increases, the time it takes for the next wave to pass a point is longer, so the period increases.

Since the period is longer, there are fewer waves passing per second, so the frequency will decrease.

The wavelength of a longitudinal wave is the distance between two consecutive areas of compression. Its unit is metre (m).

As the wavelength of sound grows longer, the frequency of the sound will decrease. This we hear as a fall in pitch from a higher note to a lower note. That is why as a guitar string is made shorter the sound gets higher in pitch.

The frequency of a wave is how many wave crests (for transverse waves) or compression zones (longitudinal waves) pass a fixed point in a second.

As the frequency of sound increases, the sound gets higher in pitch. That is why a piano has the longest strings on the left-hand side, to play the lower notes, and the strings get gradually shorter as the hands move up the keyboard.

As the frequency of light increases, the light changes colour, and very high frequency becomes x-ray or gamma radiation.

Higher frequency has higher energy. That is why radio waves (low frequency) are harmless, but ultraviolet and x-rays (higher frequency) can be dangerous.

Since the frequency is the number of waves passing a point per second, the period is the inverse of the frequency. For example, if two people pass the door per second, the interval between the people is half a second. If four pass per second, the time between them, or period, is 1/4 s.

Therefore, $f = 1/T$, where f is the frequency, and T is the period.

The period is measured in seconds, so the frequency unit is $1/s$, or 'waves per second'. In the S.I. unit system, this has a special name: hertz (Hz).

The frequency and the wavelength are inversely proportional. This means that if one increases, the other decreases.

This can be written: $f ∝ 1/λ$

The frequency is also the inverse of the period: $f = 1/T$, where f is the frequency, and T is the period.

The period, T, is measured in seconds, so the frequency unit is $1/s$, or 'waves per second'. In the S.I. unit system, this has a special name: hertz (Hz).

If we know the speed of a wave, *v* ($m/s$), then we can calculate the wavelength, *λ* (m), from the frequency, *f* (Hz), or the frequency from the wavelength, using the formula:

$$v = f⋅λ$$

The amplitude of a wave is a measure of the intensity of the energy the wave carries. For example, a note played on a musical instrument may be played louder (greater amplitude) without changing the pitch (frequency), wavelength, or velocity (sound in air is a constant 340 m/s).

The amplitude has no affect on the wavelength, frequency, period, or speed of a wave.

Christian Andreas Doppler, 29 Nov 1803 - 17 March 1853, Austrian physicist.

Doppler gave his name to the phenomenon of changing perceived frequency of a wave-emitting source as it moves at velocity towards a receiver. The change in frequency compared to the static frequency as perceived by the listener or observer is proportional to the velocity.

The Doppler Effect is used to determine the velocity of distant galaxies and the relative speeds of binary stars. Objects moving at high speed away from the observer display a red shift (overall decrease in their spectra frequency range), while moving towards the observer causes an increase in frequency, or a blue shift.

A static source sends waves at speed c towards a receiver. The formula v = f⋅λ gives the frequency $f = c/{λ}$.

The frequency as perceived by the receiver is $f_0 = {f_s}/{1 - {v_s}/c}$.

For a source moving away from the receiver, the frequency is $f_0 = {f_s}/{1 + {v_s}/c}$.

The Doppler Effect is used to measure the velocity of receding galaxies. The technique was invented by Edwin Hubble in 1929, and led to the theory that the universe was expanding, rather than remaining fixed in size, as had previously been assumed.

If the speed of the observer or the emitter is comparable to the speed of light, relativity has a significant influence on the change in frequency.

However, at lower speeds, the relationship is:

$$Δf = v/c⋅f$$where c is the speed of light in a vacuum, $3.0 x 10^8 m/s$.

Content © Renewable-Media.com. All rights reserved. Created : August 31, 2014 Last updated :March 5, 2016

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Mathematics is the most important tool of science. The quest to understand the world and the universe using mathematics is as old as civilisation, and has led to the science and technology of today. Learn about the techniques and history of mathematics on ScienceLibrary.info.

1687 - 1759

Nicolaus Bernoulli (I) was the first Nicolaus in the illustrious family dynasty of Bernoulli mathematicians in Basel, Switzerland, in the 17th and 18th centuries.

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