# Relationship among frequency amplitude wavelength and wave velocity

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In a dispersive medium, the phase speed itself depends upon the frequency of the wave, making the relationship between wavelength and frequency nonlinear. You need to be able to see the specific “faces” that each wave can have, based on three important characteristics: frequency, wavelength, and amplitude. On a longitudinal wave, the wavelength is measured as the distance between the we are really multiplying 1/s and m which gives us m/s, the velocity of the wave!. Describe the relationship between the speed of sound, its frequency, and its like all waves, travels at a certain speed and has the properties of frequency and .

The variation in speed of light with vacuum wavelength is known as dispersionand is also responsible for the familiar phenomenon in which light is separated into component colors by a prism. Separation occurs when the refractive index inside the prism varies with wavelength, so different wavelengths propagate at different speeds inside the prism, causing them to refract at different angles. The mathematical relationship that describes how the speed of light within a medium varies with wavelength is known as a dispersion relation.

Nonuniform media[ edit ] Various local wavelengths on a crest-to-crest basis in an ocean wave approaching shore [11] Wavelength can be a useful concept even if the wave is not periodic in space. For example, in an ocean wave approaching shore, shown in the figure, the incoming wave undulates with a varying local wavelength that depends in part on the depth of the sea floor compared to the wave height.

### Explain the relationship among frequency, amplitude, wavelength & wave velocity? | Yahoo Answers

The analysis of the wave can be based upon comparison of the local wavelength with the local water depth. The figure at right shows an example. Look at the following diagram Figure 1 Any of the parts of the wave that are pointing up like mountains are called crests. Any part that is sloping down like a valley is a trough. Wavelength is defined as the distance from a particular height on the wave to the next spot on the wave where it is at the same height and going in the same direction.

Usually it is measured in metres, just like any length. Most people do like to measure from one crest to the next crest or trough to troughjust because they are easy to spot. Figure 2 On a longitudinal wave, the wavelength is measured as the distance between the middles of two compressions, or the middles of two expansions.

### Wavelength - Wikipedia

Figure 3 This leads us to one of the most important formulas you will use when studying waves. Frequency tells us how many waves are passing a point per second, the inverse of time.

Wavelength tells us the length of those waves in metres, almost like a displacement. A wave is measured to have a frequency of 60Hz. If its wavelength is 24cm, determine how fast it is moving.

There is always an antinode positioned between two adjacent nodes. Antinodes are points of maximum positive and negative displacement. In such standing wave patterns, there is a unique half-number relationship between the length of the medium and the wavelength of the waves which have established the pattern which is present in the medium.

These relationships are shown below for the standing wave patterns having one node first harmonictwo nodes second harmonic and three nodes third harmonic. Other patterns for four nodes and more could be drawn by simply extending the principles which have been used for the first three patterns.

From the pattern and knowledge of the length of the medium, the wavelength can be determined using the above equations. Similarly, the length of the medium can be determined from the wavelength.

A more detailed and exhaustive discussion of the mathematics of standing wave patterns can be found at The Physics Classroom Tutorial. Wave Interference The meeting up of two waves while traveling in opposite directions along the same medium is known as interference.

When two waves interfere, the medium takes on a new resultant shape which reflects the simultaneous influence of both waves upon the particles of the medium.

The amount of displacement of the individual particles can be determined using the principle of superposition.

According to this principle, the displacement of an individual particle at a moment in time is simply the algebraic sum of the displacements that the particle would have as a result of the individual waves. So if wave A has a crest which meets up with a trough of wave B at a given location and a specified moment in time, then the displacement of the medium at that location is simply the sum of wave A's amplitude and wave B's amplitude.

## The Wave Equation

In this case, Wave B would have a negative amplitude since it is a trough; and so a positive amplitude and a negative amplitude would be added together to determine the displacement of the medium at that location and moment in time.

A more detailed and exhaustive discussion of wave interference and the principle of superposition can be found at The Physics Classroom Tutorial. Boundary Behavior Mechanical waves travel through a medium water, string, rope, snakey. The medium does not extend through space forever; eventually a medium ends. For instance, a rope may be terminated at wall to which it is tied, thus forming a boundary with a different medium the wall.

Or the end of a snakey may be tied to the end of another snakey, thus forming a boundary between two snakeys. As a wave reaches such a boundary, a portion of its energy is transmitted into the new medium and a portion of its energy is reflected off the boundary back into the original medium.

This is known as boundary behavior. As a result of the reflection and transmission, changes in amplitude, wavelength and speed can often be observed. Most commonly, one observes that a transmitted wave or pulse has a different wavelength and speed than the incident wave or pulse. While wavelength and speed may change as a wave is transmitted across a boundary, the frequency remains the same.