# Relationship between velcity, wavelength, and frequency

#### Dunkaroos

what happens to the velocity, wavelength, and frequency as you pass from air to water?

water to air?

air to air?

water to water?

One book tells me that veolocity is kept constant only within a single medium while another book says that these 3 quantities ALWAYS obey the equation (velcity = wavelength*fequency)

Also, is there a special name for this formula?

Thank You VERY much for reading/helping!

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#### Doc Al

Mentor
Dunkaroos said:
what happens to the velocity, wavelength, and frequency as you pass from air to water?

water to air?

air to air?

water to water?
What do you think? Hint: One of those three remains constant.

One book tells me that veolocity is kept constant only within a single medium while another book says that these 3 quantities ALWAYS obey the equation (velcity = wavelength*fequency)
Both are true statements. That equation is often loosely called the "wave equation".

#### berkeman

Mentor
Once in a homogeneous medium, the three quantities are related by that equation as shown. BTW, I can never remember the equation, so I use the units of the three quantities to help me get it right:

v [m/s] = wavelength [m] * frequency [1/s]

When passing from one medium to another (or to different densities within the same medium), these quantities can change. If the transition is over a distance which is much greater than a wavelength (like as sound goes straight up in the atmosphere into thinner and thinner air), then this equation still holds at any particular spot. But if the transition zone is on the order of a wavelength, I don't think that the equation is very meaningful at the transition (I could be wrong about that though).

So how does the speed of sound vary with the density of the air? Does sound go faster in water or air? You can goodle those pretty easily if you don't know already.

#### nrqed

Science Advisor
Homework Helper
Gold Member
Dunkaroos said:
what happens to the velocity, wavelength, and frequency as you pass from air to water?

water to air?

air to air?

water to water?

One book tells me that veolocity is kept constant only within a single medium while another book says that these 3 quantities ALWAYS obey the equation (velcity = wavelength*fequency)

Also, is there a special name for this formula?

Thank You VERY much for reading/helping!
You are taking about an electromagnetic wave?

In any case, both of your books are right.
The key point is that the frequency does not change when the wave changes medium. But both the speed and the wavelength will change in such a way that the equation that you wrote remains satisfied in all media.
(I am not aware of any special name for this equation...It's the equation for the speed of a sinusoidal wave).

#### Dunkaroos

Yes, electromagnetic.

Can it be concluded that the frequency of a particular wave usually remains the same?

Lets say I two waves (a 1m wavelength waveand a 2m wavelength wave) start in the same position and end in the same position. Which one will reach the end position?

Since both waves are traveling through the same medium (air), won't the velocities of the 2 waves be the same? Can I say that the velocity is independent of wavelength and frequency in a single medium?

^_^!

#### Hootenanny

Staff Emeritus
Science Advisor
Gold Member
Dunkaroos said:
Can it be concluded that the frequency of a particular wave usually remains the same?
Frequency is determined by the source.

~H

#### Dunkaroos

What do you mean by source? Example?

#### nrqed

Science Advisor
Homework Helper
Gold Member
Dunkaroos said:
Yes, electromagnetic.

Can it be concluded that the frequency of a particular wave usually remains the same?

Lets say I two waves (a 1m wavelength waveand a 2m wavelength wave) start in the same position and end in the same position. Which one will reach the end position?

Since both waves are traveling through the same medium (air), won't the velocities of the 2 waves be the same? Can I say that the velocity is independent of wavelength and frequency in a single medium?

^_^!
yes, when a wave changes medium, the frequency remains the same.

And yes, the speed is determined by the properties of the medium (for an em wave, the speed is c/n where n is the index of refraction. For a wave on a string, the speed is the square root of (the tension over the linear mass density), for a sound wave, the speed depends on the bulk modulus and the volume mass density, etc.

#### berkeman

Mentor
Dunkaroos said:
What do you mean by source? Example?
A speaker for sound. A light bulb for photons. An antenna for E&M. A binary star for gravity waves.

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