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Frequency and wavelength

Wavelength

Transverse Waves

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

Graph of a transverse wave
A transverse wave may be plotted against time. The period of the wave is the time interval between two successive wave crests passing a point.

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.

Longitudinal Waves

Wavelength
A longitudinal wave is a wave of compression passing through a medium.

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.

Frequency

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 freqency 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 Maths

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:

$$v = f⋅λ$$

Transverse waveform
The velocity of a wave is equal to the product of its wavelength and frequency.

Amplitude

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.

Diffraction Patterns

Interference patterns from diffraction
Interference patterns from diffraction, caused by waves from two sources, or parallel waves passing through two narrow slits

When straight waves pass through two narrow slits, or two point sources generate waves, the waves interfere. When they both have a peak in one place, these add together, and the result is a high wave. this is called constructive interference.

When the peak of one wave is overlaid with the trough of another wave, they cancel each other out. This is called destructive interference.

The result is a series of light and dark lines on a screen, representing the alternating constructive and destructive wave pattern resulting from two-source diffraction.

Light also produces a diffraction pattern when a parallel beam of light passes through two narrow slits close together in a barrier. A screen shows light and dark bands.

Content © Andrew Bone. All rights reserved. Created : December 19, 2013 Last updated :March 5, 2016

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