What is the frequency of a longitudinal wave in terms of distance and speed?

In summary: Therefore, λ=v/2In summary, the frequency of a longitudinal wave is the number of cycles per second.
  • #1
Kyros
2
0

Homework Statement


A longitudinal wave is propagated through a medium. The distance from one max compression to the next is X meters, and its speed is Y m/s. Express the frequency of the waves in terms of x and y.

Homework Equations


velocity of a wave= Wavelength x Frequency
Velocity of a wave = Wave length/ Period

The Attempt at a Solution


if x = the distance, then would that mean its the wave length?
and if y= speed, that would be the velocity.
therefore, if you were to express the frequency would it just be
(Rearrange for F)
Frequency= Y/X?
 
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  • #2
Kyros said:

Homework Statement


A longitudinal wave is propagated through a medium. The distance from one max compression to the next is X meters, and its speed is Y m/s. Express the frequency of the waves in terms of x and y.

Homework Equations


velocity of a wave= Wavelength x Frequency
Velocity of a wave = Wave length/ Period

The Attempt at a Solution


if x = the distance, then would that mean its the wave length?
and if y= speed, that would be the velocity.
therefore, if you were to express the frequency would it just be
(Rearrange for F)
Frequency= Y/X?
Welcome to the PF.

Looks good to me. Another trick to help with this kind of question is to use units:

Distance X is in [m]
Frequency is in Hertz [1/s]
Velocity is in [m/s]

So the units check out, F [1/s] = Y [m/s] / X [m]

BTW, this is a good general technique to use in all of your work in science and math. Carry the units along in your calculations, to keep checking that your equations make sense as you formulate and simplify them.

:smile:
 
  • #3
As berkeman wrote, dimensional/units analysis will get you a long way, but it leaves open the possibility of a wrong constant factor.
To see that it is v/λ (velocity/wavelength), consider standing at one point as one whole wavelength goes past you. You will see the amplitude go from max one way to max the other way, then back to max the first way again. That will take time λ/v and you have observed one full cycle.
 

Related to What is the frequency of a longitudinal wave in terms of distance and speed?

What is a longitudinal wave?

A longitudinal wave is a type of wave where the disturbance or vibration of the medium is in the same direction as the direction of wave propagation. This means that the particles of the medium move back and forth parallel to the direction of the wave.

What are some examples of longitudinal waves?

Some examples of longitudinal waves include sound waves, seismic waves, and pressure waves in fluids. These waves are characterized by areas of compression and rarefaction as they travel through a medium.

How do longitudinal waves differ from transverse waves?

Unlike longitudinal waves, transverse waves have a disturbance or vibration of the medium that is perpendicular to the direction of wave propagation. This means that the particles of the medium move up and down or side to side as the wave passes through.

What is the wavelength of a longitudinal wave?

The wavelength of a longitudinal wave is the distance between two consecutive points of maximum compression or rarefaction. It is typically measured in meters (m) and can vary depending on the frequency and velocity of the wave.

What is the speed of a longitudinal wave?

The speed of a longitudinal wave is determined by the properties of the medium through which it is traveling. In general, it is directly proportional to the frequency and wavelength of the wave. In a uniform medium, the speed of a longitudinal wave is given by the formula v = fλ, where v is the speed, f is the frequency, and λ is the wavelength.

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