Understanding Wave Frequency and Tension: V=fλ vs V=√T/μ

In summary, the conversation discusses the difference between two equations that relate the physical relationship of a wave to its frequency, wavelength, and velocity of propagation. It is explained that one equation relates to the physical properties of the transmission media, such as tension and mass/length, while the other relates to the physical relationship of the wave. It is stated that changing the frequency of the wave does not affect the properties of the media, and therefore, the only thing that can change is the wavelength. The conversation also includes a real-life example and a link to a derivation of the equation v^2 = T/m.
  • #1
tanzl
61
0

Homework Statement


I do not understand the difference between v=f [tex]\lambda[/tex] and v=[tex]\sqrt{T/\mu}[/tex]
If a string is vibrated twice the frequency but the same tension as previous. Would the speed of the wave doubled?
 
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  • #2
One equation relates the physical relationship of the wave - frequency, wavelength to velocity of propagation.

The other relates the velocity to the physical properties of the transmission media Tension and mass/length to the velocity of propagation.

Which properties can affect the speed of propagation? If you change the frequency of the wave how would you have affected the properties of the media that determine speed of propagation?
 
  • #3
tanzl said:
If a string is vibrated twice the frequency but the same tension as previous. Would the speed of the wave doubled?

No. Yhe wacelength would be halved.
 
  • #4
If the both equations are true for the string. The only way to have same tension and thus same speed but different frequency would be a different wavelength. But, that is from equation. How can I prove it or derive it? or maybe a more concrete example. Thanks.
 
  • #5
A train has many trucks, each L metres long. If f trucks pass per second,
how fast is the train going?
 
  • #6
v=Lf
L is wavelength and f is frequency.
I understand this equation but I confused the two.
In your example, if I increase f the speed will increase but it is not the case in a string.
I am not convinced that by doubling the frequency of the vibration the speed of the wave is still the same.
 
  • #7
The point is that changing the frequency changes no property of the wire, and it is the physical property of the wire that determines the speed of propagation. Namely force and mass distribution.

The statement says Tension is the same. Same wire. Same mass per length. Same velocity of propagation.

Hence the only thing that can change if you change frequency is λ.
 

FAQ: Understanding Wave Frequency and Tension: V=fλ vs V=√T/μ

1. What is wave frequency?

Wave frequency refers to the number of complete wave cycles that occur in one second. It is measured in Hertz (Hz) and is inversely proportional to the wavelength. This means that as the frequency increases, the wavelength decreases.

2. What is the relationship between wave frequency and tension?

The relationship between wave frequency and tension can be described by the formula V=√T/μ, where V is the wave velocity, T is the tension, and μ is the linear mass density of the medium. This formula shows that as the tension increases, the wave velocity also increases, resulting in a higher frequency.

3. How does wave tension affect the wavelength?

Wave tension does not directly affect the wavelength. However, it does affect the wave velocity, which in turn affects the wavelength. As the wave velocity increases, the wavelength decreases, and vice versa.

4. What is the difference between V=fλ and V=√T/μ?

V=fλ is the formula for calculating wave velocity using frequency and wavelength, while V=√T/μ is the formula for calculating wave velocity using tension and linear mass density. These formulas are derived from different equations and are used to describe different aspects of wave behavior.

5. How do frequency and tension impact the properties of a wave?

Frequency and tension both play important roles in determining the properties of a wave. A higher frequency results in a shorter wavelength and a more energetic wave, while a higher tension results in a higher wave velocity and a steeper wave. These factors also influence the propagation and interference of waves.

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