# Relationship between frequency and wavelength [closed]

I am currently writing up a report for science class on the relationship between frequency and wavelength. And so I was wondering if anyone knew where I could find published results (literature value) and I would like to know if it is a theory or a law (presumably) and who's theory/law it is?

Thanks.

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## closed as off-topic by John Rennie, Waffle's Crazy Peanut, tpg2114, Qmechanic♦Oct 31 '13 at 17:13

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You won't find published results because this is elementary physics and is covered in any physics textbook. Velocity = frequency times wavelength:

$$v = f\lambda$$

This is particularly useful for light, where the velocity is the speed of light, because then you have the relationships between the two:

$$f = \frac{c}{\lambda}$$

$$\lambda = \frac{c}{f}$$

I'd guess your teacher intends your report to explore this relationship and explain why it's true. Some creative Googling should help.

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The relationship between frequency and wavelength is covered in any physics textbook as you can read in the well expressed answer of John Rennie.

Interpretation of the equation in which is expressed that the wave velocity equals the frequency multiplied by the wavelength [ in common wave propagation theory in physics ].

Take for example (sound):

With the travelling wave equation: the propagation velocity of the wave [in m/s] equals the frequency [in Hz] multiplied by the wavelength [in m].

This equation must be interpreted in the following way: the speed of a (sound) wave that moves through a medium isn’t dependent on its frequency and its wavelength.

The speed (of sound) – hence also the speed with which (sound) energy is transported – is a material constant and it therefore only depends on a number of properties of that medium. And the only way to change that speed is to change the properties of the medium.

Once the speed (of sound) in a medium is determined the above mentioned equation expresses the relation between the (sound) frequency and the wavelength.

The two have an inverse relationship.

• Given the frequency of the wave, the wavelength is equal to the speed (of sound) in the medium divided by the frequency.

Or in reverse:

• Given the wavelength of the wave, the frequency is equal to the speed (of sound) in the medium divided by the wavelength.

In textbooks you can read: The speed of sound in fluids and solids is given by the square route of the compressibility modulus [in Pascal] divided by the density [in kg/m³]. As an indication: this results in a speed velocity of 1858 m/s for glycerin and 870 m/s for paraffin oil.

You can see that the wave propagation velocity in a medium, the acoustic vibration frequency and the corresponding wavelength have the following common basic relation: the wave propagation velocity equals the acoustic vibration frequency multiplied by the corresponding wavelength.

This relation is one of the fundamental corner stones of common wave propagation theory in physics.

For the definition of a wave you can than look in the Webster Dictionary.

Webster Dictionary Definition of a Wave.

Webster's dictionary defines a wave as "a disturbance or variation that transfers energy progressively from point to point in a medium and that may take the form of an elastic deformation or of a variation of pressure, electric or magnetic intensity, electric potential, or temperature."

Be aware that the equation in which is expressed that the wave velocity equals the frequency multiplied by the wavelength can easily lead to a completely erroneous interpretation.

For the physics in the equation you have to be aware about for example the following:

Measuring both the wavelength in the ‘wave’ evoked by the frequency stimulus and subsequently calculating the propagation speed of the ‘wave’ by multiplying wavelength with frequency has for example nothing to do with correct physics.

So, it is important to know: The speed of a sound wave that moves through a medium isn’t dependent on its frequency and its wavelength.

Because, the speed is given ...

Namely:

The speed of sound in fluids and solids is given by the square route of the compressibility modulus [in Pascal] divided by the density [in kg/m3]. As an indication: this results in a speed velocity of 1858 m/s for glycerin and 870 m/s for paraffin oil.

With the answer of John Rennie and maybe also with this answer you can explore the above mentioned relationship and explain your teacher and the class why it's true.

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