Relationship between velcity, wavelength, and frequency

In summary, the frequency of a particular wave usually remains constant as it passes from one medium to another. However, the velocity and wavelength may change depending on the properties of the medium. The equation velocity = wavelength * frequency, also known as the wave equation, is always satisfied for any given wave. The frequency is determined by the source of the wave, such as a speaker or a light bulb. The velocity of a wave is independent of its wavelength and frequency within a single medium.
  • #1
Dunkaroos
19
0
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?

:rolleyes: Thank You VERY much for reading/helping!
 
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  • #2
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".
 
  • #3
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.
 
  • #4
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?

:rolleyes: 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).
 
  • #5
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?

^_^!
 
  • #6
Dunkaroos said:
Can it be concluded that the frequency of a particular wave usually remains the same?

Frequency is determined by the source.

~H
 
  • #7
What do you mean by source? Example?
 
  • #8
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.
 
  • #9
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.
 

What is the relationship between velocity, wavelength, and frequency?

The relationship between velocity, wavelength, and frequency is described by the wave equation: v = λf, where v is the velocity of the wave, λ (lambda) is the wavelength, and f is the frequency. This equation shows that as the velocity increases, either the wavelength or the frequency must also increase to maintain a constant value for v.

How does the velocity of a wave affect its wavelength and frequency?

The velocity of a wave has a direct relationship with its wavelength and frequency. As the velocity of a wave increases, the wavelength must also increase to maintain a constant frequency. Likewise, if the velocity decreases, the wavelength must decrease to maintain a constant frequency.

What is the significance of wavelength and frequency in a wave?

Wavelength and frequency are important properties of a wave that describe its characteristics. Wavelength is the distance between two consecutive points on a wave that are in phase, and frequency is the number of complete cycles of the wave that occur in one second. These properties help us understand and analyze different types of waves, including electromagnetic waves and sound waves.

How are wavelength and frequency related in different types of waves?

In all types of waves, there is an inverse relationship between wavelength and frequency. This means that as the wavelength increases, the frequency decreases, and vice versa. However, the exact relationship between these two properties may vary depending on the type of wave. For example, in electromagnetic waves, the wavelength is directly proportional to the frequency, whereas in sound waves, the wavelength is inversely proportional to the frequency.

How can the relationship between velocity, wavelength, and frequency be applied in real-world situations?

The relationship between velocity, wavelength, and frequency is applied in various fields, including physics, engineering, and telecommunications. For example, in telecommunications, the frequency and wavelength of a signal are used to determine the bandwidth and data transmission rate. In physics, this relationship is used to study the behavior of different types of waves, including light and sound waves. In engineering, it is used to design and optimize different systems and devices that utilize waves, such as antennas and speakers.

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