Find Maximum Transverse velocity of string

T is the period of the wave.In summary, the problem involves a string with fixed ends, a pulse traveling to the right at a speed of 40 m/sec, with a wavelength of 2 meters and an amplitude of .1 m. The equations used to solve the problem are y=A*Sin(kx-wt), where w is omega, \lambda=2*pi/k, frequency=w/2pi, velocity=w/f, and V_max=w*A. The value of k is found to be pi, but the value of w (omega) cannot be determined without the period of the wave.
  • #1
aseylys
22
0

Homework Statement


For a string of length 100m with fixed ends, a pulse is traveling to the right at a speed of 40 m/sec. The pulse has a wavelength of 2 meters and an amplitude of .1 m.


Homework Equations


y=A*Sin(kx-wt) ((where w is omega))
[itex]\lambda[/itex]=2*pi/k
frequency=w/2pi
Velocity=w/f
Velocity=f/[itex]\lambda[/itex]
V_max=w*A



The Attempt at a Solution


So I plugged in as much as I could:
y=A*Sin(kx-wt)
[itex]\lambda[/itex]=2 so 2=2pi/k ==> k=pi (?)

I can't figure out how to get w (omega). So I'm kinda stuck at a dead end. Anyone have any suggestions?
 
Last edited:
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  • #2
ω= 2∏/T radians per second
 

1. What is the maximum transverse velocity of a string?

The maximum transverse velocity of a string is the highest speed that the string can reach while oscillating in a transverse motion.

2. How is the maximum transverse velocity of a string calculated?

The maximum transverse velocity of a string can be calculated using the formula v = ωA, where v is the maximum velocity, ω is the angular frequency of oscillation, and A is the amplitude of the string's oscillation.

3. What factors affect the maximum transverse velocity of a string?

The maximum transverse velocity of a string can be affected by factors such as the tension of the string, the length of the string, and the mass per unit length of the string. Other factors, such as air resistance, can also play a role in determining the maximum velocity.

4. How does the maximum transverse velocity of a string relate to its frequency?

The maximum transverse velocity of a string is directly proportional to its frequency. This means that as the frequency of the string's oscillation increases, so does its maximum velocity.

5. What is the significance of finding the maximum transverse velocity of a string?

The maximum transverse velocity of a string is an important value to know in order to understand the behavior and properties of the string. It can also be used to calculate other important quantities, such as the kinetic and potential energy of the string.

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