Time for a wave to propagate

  • Thread starter pcjang
  • Start date
  • Tags
    Time Wave
In summary, the time for a wave to propagate is the amount of time it takes for a disturbance or energy to move through a medium from one point to another. This can be affected by the properties of the medium, wavelength and amplitude of the wave. The time for a wave to propagate is calculated using the formula: time = distance/velocity, and is not constant as it can vary due to external factors such as temperature, pressure, and obstacles or barriers in the medium.
  • #1
pcjang
3
0

Homework Statement


Show that the time it takes a wave to propagate up the cable (cable which hangs vertically under its own weight) is t = 2[tex]\sqrt{L/g}[/tex], where L is the cable length.


Homework Equations


i think... v=[tex]\sqrt{F/\mu}[/tex]



The Attempt at a Solution


i've been staring at this problem for about 2 hours now. can anyone just help me how to get started on this one??
 
Physics news on Phys.org
  • #2
pcjang said:

Homework Equations


i think... v=[tex]\sqrt{F/\mu}[/tex]

Yes. And F is the tension in the cable.
 
  • #3


As a scientist, it is important to first understand the problem and the given information. The problem states that we need to show that the time it takes for a wave to propagate up a cable (which hangs vertically under its own weight) is equal to t = 2√(L/g), where L is the cable length and g is the acceleration due to gravity.

To begin, we can use the equation for wave velocity, v = √(F/μ), where F is the force acting on the cable and μ is the linear mass density of the cable. In this case, the force acting on the cable is its weight, which is equal to mg, where m is the mass of the cable and g is the acceleration due to gravity. The linear mass density of the cable can be calculated by dividing the total mass of the cable by its length, giving us μ = m/L.

Now, we can substitute these values into the equation for wave velocity, giving us v = √(mg/mL). We can simplify this expression by canceling out the mass terms, giving us v = √(g/L).

Next, we can use the equation for wave speed, v = λf, where λ is the wavelength of the wave and f is the frequency. In this case, the wavelength of the wave can be approximated to be equal to the length of the cable, as the wave will travel from the bottom of the cable to the top and back down again. Therefore, we can rewrite the equation as v = Lf.

Now, we can combine the two equations we have derived for wave velocity, giving us Lf = √(g/L). We can solve for the frequency, f, by dividing both sides by L, giving us f = √(g/L^2).

Finally, we can use the equation for period, T = 1/f, to find the time it takes for the wave to propagate up the cable. Therefore, T = 1/√(g/L^2). Simplifying this expression gives us T = 2√(L/g), which is the desired result.

In conclusion, we have shown that the time it takes for a wave to propagate up a cable is equal to t = 2√(L/g), where L is the cable length and g is the acceleration due to gravity. This result can be helpful in understanding the behavior of waves in a vertical cable
 

What is the definition of "time for a wave to propagate"?

The time for a wave to propagate is the amount of time it takes for a disturbance or energy to move through a medium from one point to another.

What factors affect the time for a wave to propagate?

The time for a wave to propagate can be affected by the properties of the medium through which it is traveling, such as density and elasticity, as well as the wavelength and amplitude of the wave.

How is the time for a wave to propagate calculated?

The time for a wave to propagate can be calculated using the formula: time = distance/velocity, where distance is the length of the medium and velocity is the speed at which the wave is traveling.

Is the time for a wave to propagate constant?

No, the time for a wave to propagate is not constant. It can vary depending on the properties of the medium and the characteristics of the wave.

Can the time for a wave to propagate be affected by external factors?

Yes, external factors such as temperature, pressure, and the presence of obstacles or barriers can also affect the time for a wave to propagate through a medium.

Similar threads

  • Introductory Physics Homework Help
Replies
19
Views
723
  • Introductory Physics Homework Help
Replies
8
Views
500
  • Introductory Physics Homework Help
Replies
8
Views
871
  • Introductory Physics Homework Help
Replies
2
Views
629
  • Introductory Physics Homework Help
Replies
26
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
254
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
988
  • Introductory Physics Homework Help
Replies
11
Views
169
Back
Top