# Are wavelength and the distance same thing?

Can you clarify for me the following question: are wavelength and distance same?

I know wavelength is measured in terms of distance but when we have a look at the two equations: $$c=f\,\lambda\\ v=d/t$$
it actually explains the same thing where $v=c$=velocity and $1/t$ is frequency. So $\lambda$ should be equal to $d$. So if $\lambda = d$, then why do we have two equations existing instead of one. Can we use any equation to calculate velocity?

A wavelength is a particular distance, corresponding to the length travelled during a period, which is a special time. Since $v=d/t$ holds good for the distance $d$ travelled by a constant velocity object over any given time interval $t$, a fortiori this relationship holds for the special, particular time known as the period. So, yes, $v=d/t$ is how you derive $c=f\,\lambda$, but of course not every distance travelled by a disturbance has the particular significance of the wavelength.

• What does the last sentence mean? – Mohamed Osama Jun 12 '15 at 13:11
• @MohamedOsama Simply that $v=d/t$ is a general statement which you specialize to the case of wavelength. – WetSavannaAnimal Jun 12 '15 at 14:46

The relationship between wavelength and distance is similar to the relationship between frequency and duration, and no: neither pair is the same. You can see by using dimensional analysis.

Wavelength is distance divided by cycles. Frequency is cycles divided by time. Multiply the two, the cycles cancel out, and you get distance divided by time, or velocity.

For instance, if you look at a 90MHz FM radio wave (that's 9 x 10^7 cycles per second), the wavelength is about 3 1/3 meters (that's 3.333 meters per cycle). Multiply them together, and you get 3 x 10^8 meters per second. Bingo: speed of light.

• @Great explanation.Does this mean that they(don't know who) found speed of light by experimentally founding wavelength and frequency of a wave(any wave) and multiplying it to get a constant? – justin Dec 3 '15 at 9:11
• @justin No; light speeds were being measured long before there were electronics. – Daniel Griscom Dec 3 '15 at 12:00
• :Yeah that's right from the article. – justin Dec 4 '15 at 7:57

The lambda is the distance between 2 points having the same phase like two successive crests the velocity is the wave can be conceived as how many crests for example passes through a reference in a given time you can use both equations but c=f*lambda is used if you have lambda , its proof is V = distance / time , if a crest traveled a distance = wavelength then that is done in a time = T periodic time , OK that means the crest moves one cycle we have by definition the frequency = number of cycles per second so the time required for one cycle = periodic time = 1 / f substitute with it in v= d / t , you find v = lambda * f

Velocity is a more widely used term, usable for all moving objects and waves, while wavelength is of course only usable for waves.

Wavelength is the minimal distance between two points of a wave with the same phase. Take for example a sinusoidal wave: the wavelength will be the difference between two maxima or two minima.

The velocity of a wave is used more often in wave packets: a composition of waves. These can travel with a different speed than the individual sinusoidal waves. So the velocity of a wave packet will be the speed that the center of the wave packet will travel with.

In your equations, the d will also usually represent total distance, while lambda is usually a very small distance and remains fixed for a particular sinus wave. But take for example a wave which has travelled N times its wavelength lambda, and did that in a time t, then t will be N times its period. And since the period = 1/f we have: v=d/t = Nlambda/Nperiod=f*lambda.

The properties and formulas depend on what kind of waves you are talking about so I hope this is not too confusing.

Sir, One has to see the difference : wavelength is the distance of one cycle only. V is the distance travelled per second. So if there are n waves per second , v is the product of n and wavelength. eg. If we go around our house 50 rounds per second (n) and one round is 20 m ( wavelength ) we go 1000 meter per second (v). Hopes its clear now

## protected by ACuriousMind♦Aug 13 '17 at 9:04

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