Wave equation, wavelenght not given

In summary, the given data includes a wave problem with a frequency of 20 Hz and an amplitude of 0.005 m. The wave travels along a string with a length of 0.4 m and is created in 0.1 seconds. The speed of each part of the string can be calculated using the equation v = v0 cos (ωt - kx). Constants v0, ω, and k can be solved for, as well as the maximum acceleration of each part of the string. The distance between parts of the string with a phase difference of π/2 can also be found. To solve for the wavelength, one can use the equation c = ƒ λ or c = 2πf
  • #1
AncientOne99
32
1

Homework Statement


Wave problem
Given data :
f = 20 Hz
y0 = 0.005 m
t = 0.1 s
x = 0.4 m1. The end portions of stretched string oscillates in the transverse direction with a frequency of 20 Hz and an amplitude of 0.005 m. Wave , which travels along the string, made in 0.1 second, 0.4 m long path.
The speed of each part of string written by the equation v = v0 cos (ωt - kx).
a) What are the constants v0, ω and k to?
b) What is the maximum acceleration of each part of string?
c) What is the distance between the parts of the string, which varies with the phase difference Δ φ = π / 2?
d) How much time does a part of string need to travel from one extreme point to another?

Homework Equations


y(x, t) =y0sin(ωt - kx)
v(x, t)= v0cos (ωt - kx)
c = ƒ λ
ω = 2πf
k = 2π/λ

The Attempt at a Solution


I tried to solve for a wave number but i don't know how to calculate wavelenght.
I don't really well know the diferrence between these three equations for wave.
1. velocity = displacement / time
2. wave velocity = wavelenght / period
3. velocity (particle) = v0 cos (ωt - kx)
1. and 2. equation seem very similar but i don't know if they are really.
 
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  • #2
AncientOne99 said:

Homework Statement


Wave problem
Given data :
f = 20 Hz
y0 = 0.005 m
t = 0.1 s
x = 0.4 m1. The end portions of stretched string oscillates in the transverse direction with a frequency of 20 Hz and an amplitude of 0.005 m. Wave , which travels along the string, made in 0.1 second, 0.4 m long path.
The speed of each part of string written by the equation v = v0 cos (ωt - kx).
a) What are the constants v0, ω and k to?
b) What is the maximum acceleration of each part of string?
c) What is the distance between the parts of the string, which varies with the phase difference Δ φ = π / 2?
d) How much time does a part of string need to travel from one extreme point to another?

Homework Equations


y(x, t) =y0sin(ωt - kx)
v(x, t)= v0cos (ωt - kx)
c = ƒ λ
ω = 2πf
k = 2π/λ

The Attempt at a Solution


I tried to solve for a wave number but i don't know how to calculate wavelenght.
I don't really well know the diferrence between these three equations for wave.
1. velocity = displacement / time
2. wave velocity = wavelenght / period
3. velocity (particle) = v0 cos (ωt - kx)
1. and 2. equation seem very similar but i don't know if they are really.
What does this sentence mean?
Wave , which travels along the string, made in 0.1 second, 0.4 m long path.
How do you get the speed of the wave from this information?
 
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Likes AncientOne99
  • #3
AncientOne99 said:
Speed of wave = displacement of wave / time elapsed
I was thinking about similarity between
velocity of wave and speed of wave so like:

c = 20 Hz * λ
v = 0.1s * 0.4m

And then I equal c and v is the next step.
c=v and from that calculated λ but i don't know if i can do that, i don't have any knowledge about partial derivatives and y(x,t) functions from math.
Any suggestions?
 
  • #4
AncientOne99 said:
v = 0.1s * 0.4m
Speed is not distance times time. What is it?
 
  • #5
v = 0.4m/0.1s = 4m/s
 
  • #6
AncientOne99 said:
v = 0.4m/0.1s = 4m/s
Good. Can you find the wavelength now?
 
  • #7
Yes i equal two equations.
 

Related to Wave equation, wavelenght not given

1. What is the wave equation?

The wave equation is a mathematical formula that describes the behavior of waves, including sound and light waves. It is typically written as d2u/dt2 = c2 * d2u/dx2, where u represents the wave, t is time, and x is the position of the wave along the medium. The constant c represents the speed of the wave.

2. How is the wave equation used?

The wave equation is used to predict the behavior of waves in different mediums. It can also be used to calculate the speed, wavelength, and frequency of a wave. Additionally, it is used in various fields of science, including acoustics, optics, and electromagnetism.

3. What is the relationship between wavelength and the wave equation?

The wave equation does not directly include the wavelength, but it is related to the wavelength through the wave's speed. The wavelength can be calculated by dividing the wave's speed by its frequency, which is represented by c/ƒ in the wave equation.

4. Can the wave equation be used for all types of waves?

The wave equation can be used for different types of waves, as long as they follow the same basic principles. It is commonly used for mechanical waves, such as sound waves, and electromagnetic waves, such as light waves. However, it may not accurately describe the behavior of all types of waves, such as quantum waves.

5. What happens if the wavelength is not given in the wave equation?

If the wavelength is not given in the wave equation, it can be calculated using other variables, such as the wave's speed and frequency. However, it is important to note that the wavelength is a crucial component in fully understanding and predicting the behavior of waves, so it is usually provided or measured in experiments and calculations.

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