العلوم
Wavelength: One Whole Wave, Measured Peak to Peak
Wavelength is the length of one complete wave, crest to crest. Its symbol is λ, its unit is the metre, and it connects to speed and frequency through v = fλ.
Wavelength
Wavelength is the distance between one point on a wave and the identical point on the next wave, such as from one crest to the next crest.
- يُسمّى أيضاً
- Lambda, λ
- أين يقابله الطلاب
- Grade 7 science, on the first labelled wave diagram, and again in Grade 9 physics in every calculation using the wave equation.
الإجابة باختصار
Wavelength is the length of one complete wave: the distance from a point on one wave to the matching point on the next, most often measured crest to crest. Its symbol is the Greek letter λ and its unit is the metre. It links to wave speed and frequency through the equation v = fλ.
مثال
λ = v ÷ f = 340 ÷ 170 = 2 m
Taking the speed of sound in air as 340 metres per second, a note of frequency 170 hertz has a wavelength of 2 metres. The reasoning behind the division is worth holding on to: 170 whole waves are produced every second and the front of the first one has travelled 340 metres in that time, so those 170 waves are spread along 340 metres, giving 2 metres each.
One whole wave, from anywhere to the matching anywhere
The usual measurement is crest to crest, but nothing special is happening at the crest. Trough to trough gives the same answer, and so does any point to the identical point on the next wave — the same height, moving the same way. What is being measured is the length of the repeating pattern.
The common error is measuring crest to trough. That is half a wavelength, because it is only half of the pattern. On a longitudinal wave such as sound, where the particles move back and forth rather than side to side, the equivalent measurement is from one compression to the next compression.
The symbol and the units
Wavelength is written λ, the Greek letter lambda, which acts as the l of length. The SI unit is the metre, and every calculation using the wave equation needs it in metres before anything else happens.
The practical unit varies enormously with the wave, and this is where conversions bite. Water waves are measured in metres. Visible light runs from roughly 400 nanometres at the violet end to about 700 nanometres at the red, and a nanometre is a billionth of a metre. Long-wave radio is measured in hundreds of metres. Converting to metres first, rather than at the end, prevents most of the errors here.
Finding it with the wave equation
The wave equation is v = fλ: speed equals frequency times wavelength. Rearranged, λ = v ÷ f. An FM radio station broadcasting at 100 megahertz sends waves that travel at 3 × 10⁸ metres per second, so the wavelength is 3 × 10⁸ ÷ 1 × 10⁸ = 3 metres, roughly the length of a small car.
One consequence is worth remembering because it saves work. All electromagnetic waves travel at the same speed in a vacuum, so across that whole spectrum wavelength and frequency are locked together: long wavelength means low frequency. Radio waves are measured in metres and kilometres and have the lowest frequencies; gamma rays have wavelengths smaller than an atom and the highest.
- Approximate wavelength range of visible light, violet at the short end and red at the long
- 400–700 nmApproximate wavelength range of visible light, violet at the short end and red at the long
أسئلة شائعة
What is the symbol for wavelength?
The Greek letter lambda, written λ. It appears in the wave equation as v = fλ and on labelled wave diagrams as the arrow spanning one complete wave. Using an ordinary letter such as w or l is not wrong in your own notes, but λ is what an exam paper will use.
Is wavelength measured from crest to trough?
No. Crest to trough is half a wavelength, because it covers only half the repeating pattern. Measure crest to crest, or trough to trough, or between any two identical points on consecutive waves. A quick check: a full wavelength contains one crest and one trough, not one of them alone.
How do you calculate wavelength from frequency?
Divide the wave speed by the frequency: λ = v ÷ f, rearranged from v = fλ. Both must be in matching units, so speed in metres per second and frequency in hertz gives a wavelength in metres. A frequency given in kilohertz or megahertz must be converted to hertz before dividing.
Does wavelength change when light enters glass?
Yes. Light slows down in glass while its frequency stays exactly the same, and since v = fλ, a smaller speed with an unchanged frequency means a shorter wavelength. That change of speed at the boundary is what bends the ray, which is refraction. The colour does not change, because colour follows frequency.
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