Velocity, Amplitude, Wavelength, And Frequency - The Measures Of A Wave
A progressive wave is represented as y=a Sin (wt-kx) Here, * y=instantaneous displacement of a particle participating in the wave propagation. Any combinations of frequencies and amplitudes are allowed. signal occurs between source as listener, wave velocity is generally constant. Exp Brain Res. Jan 18;31(1) The relationship between speed and amplitude of the fastest voluntary contractions of human arm muscles. Freund HJ .
In the case of a slinky wave, the disturbance can be seen traveling back to the original end. A slinky wave that travels to the end of a slinky and back has doubled its distance. That is, by reflecting back to the original location, the wave has traveled a distance that is equal to twice the length of the slinky.
Energy Transport and the Amplitude of a Wave
Reflection phenomena are commonly observed with sound waves. When you let out a holler within a canyon, you often hear the echo of the holler.
The sound wave travels through the medium air in this casereflects off the canyon wall and returns to its origin you. The result is that you hear the echo the reflected sound wave of your holler. A classic physics problem goes like this: Noah stands meters away from a steep canyon wall. He shouts and hears the echo of his voice one second later.
What is the speed of the wave? Remember, when there is a reflection, the wave doubles its distance. In other words, the distance traveled by the sound wave in 1 second is equivalent to the meters down to the canyon wall plus the meters back from the canyon wall.
Variables Affecting Wave Speed What variables affect the speed at which a wave travels through a medium? Does the frequency or wavelength of the wave affect its speed? Does the amplitude of the wave affect its speed? Or are other variables such as the mass density of the medium or the elasticity of the medium responsible for affecting the speed of the wave? These questions are often investigated in the form of a lab in a physics classroom. The more displacement that is given to the first coil, the more amplitude that it will have.
So in the end, the amplitude of a transverse pulse is related to the energy which that pulse transports through the medium.
What is the relationship between amplitude and speed of a wave?
Putting a lot of energy into a transverse pulse will not effect the wavelength, the frequency or the speed of the pulse. The energy imparted to a pulse will only affect the amplitude of that pulse. Consider two identical slinkies into which a pulse is introduced.
If the same amount of energy is introduced into each slinky, then each pulse will have the same amplitude. But what if the slinkies are different?
What is the relationship between amplitude and speed of a wave? | Yahoo Answers
What if one is made of zinc and the other is made of copper? Will the amplitudes now be the same or different? If a pulse is introduced into two different slinkies by imparting the same amount of energy, then the amplitudes of the pulses will not necessarily be the same.
In a situation such as this, the actual amplitude assumed by the pulse is dependent upon two types of factors: Two different materials have different mass densities. The imparting of energy to the first coil of a slinky is done by the application of a force to this coil.
More massive slinkies have a greater inertia and thus tend to resist the force; this increased resistance by the greater mass tends to cause a reduction in the amplitude of the pulse.
Different materials also have differing degrees of springiness or elasticity.
A more elastic medium will tend to offer less resistance to the force and allow a greater amplitude pulse to travel through it; being less rigid and therefore more elasticthe same force causes a greater amplitude. Energy-Amplitude Mathematical Relationship The energy transported by a wave is directly proportional to the square of the amplitude of the wave.
This energy-amplitude relationship is sometimes expressed in the following manner. This means that a doubling of the amplitude of a wave is indicative of a quadrupling of the energy transported by the wave. A tripling of the amplitude of a wave is indicative of a nine-fold increase in the amount of energy transported by the wave.
And a quadrupling of the amplitude of a wave is indicative of a fold increase in the amount of energy transported by the wave. The table at the right further expresses this energy-amplitude relationship. Observe that whenever the amplitude increased by a given factor, the energy value is increased by the same factor squared. For example, changing the amplitude from 1 unit to 2 units represents a 2-fold increase in the amplitude and is accompanied by a 4-fold 22 increase in the energy; thus 2 units of energy becomes 4 times bigger - 8 units.
As another example, changing the amplitude from 1 unit to 4 units represents a 4-fold increase in the amplitude and is accompanied by a fold 42 increase in the energy; thus 2 units of energy becomes 16 times bigger - 32 units.