Wave Speed Equation: Solve Homework w/ Max Displacement 0.16m

In summary, the given equation represents a moving pulse with x and y as units of meter and t as units of second. The options to choose from are whether the pulse is moving in a positive x axis, the displacement of the pulse after 2 seconds, the maximum displacement of the pulse, and whether the pulse is symmetric. The velocity of the pulse is 1.25m/s towards the negative x axis. To determine the amplitude, the shape of the pulse needs to be known and it can be graphed to determine the other options. At t=0, the pulse is symmetric to the y-axis with a maximum displacement of 0.16m. To determine the maximum displacement at a different time, the function y(x)=
  • #1
Hydrous Caperilla
62
7

Homework Statement



y(x,t)=0.8/{(4x+5t)^2+5 }represents a moving pulse,where x and y are in metre and tin second.Then choose the options.

(a)Pulse is moving in positive X axis
(b)In 2 secs,it will travel a displacement of 2.5m
(c)It's maximum displacement is 0.16m
(d)It is a symmetric pulse

Homework Equations

The Attempt at a Solution



So since it is a general transverse wave so it's velocity is 1.25 towards negative X axis.

I can't say about the amplitude unless I know the shape of the pulse so How should I graph this and work out the other options
 
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  • #2
There is no t in the equation.
 
  • #3
My mistake...sorry
 
  • #4
Hydrous Caperilla said:

Homework Statement



y(x,t)=0.8/{(4x+5t)^2+5 }represents a moving pulse,where x and y are in metre and tin second.Then choose the options.

(a)Pulse is moving in positive X axis
(b)In 2 secs,it will travel a displacement of 2.5m
(c)It's maximum displacement is 0.16m
(d)It is a symmetric pulse

Homework Equations

The Attempt at a Solution



So since it is a general transverse wave so it's velocity is 1.25 towards negative X axis.

I can't say about the amplitude unless I know the shape of the pulse so How should I graph this and work out the other options
How does it look at t=0?
 
  • #5
ehild said:
How does it look at t=0?
At t=0,y is 0.16m
 
  • #6
Hydrous Caperilla said:
At t=0,y is 0.16m
At ##t=0##, ##y## is a function of ##x##.
 
  • #7
I got the graph and it looks symmetric to Y axis with y=0.16 m at t=0
 
  • #8
Hydrous Caperilla said:
I got the graph and it looks symmetric to Y axis with y=0.16 m at t=0
You should calculate the position xmax of the maximum of y (it will be a function of t), and then the value of y(xmax,t). That will tell you what the maximum displacement is. You can then check the symmetry of y around xmax.
 
  • #9
Hydrous Caperilla said:
I got the graph and it looks symmetric to Y axis with y=0.16 m at t=0

Yes, it is symmetric to the Y axis at t=0. At what x does the function $$ y(x)=\frac{0.8}{(4x)^2+5} $$ have its maximum, and what is the maximum displacement from equilibrium?
At what x is the maximum of y(x,t) at a different time, at t = 2 s, for example?
 

1. What is the wave speed equation?

The wave speed equation is a mathematical formula that calculates the speed of a wave based on its frequency and wavelength. It is represented as v = fλ, where v is the wave speed, f is the frequency, and λ is the wavelength.

2. How do you solve homework involving the wave speed equation?

To solve homework involving the wave speed equation, you first need to identify the known values of frequency and wavelength. Then, you can plug those values into the equation v = fλ to calculate the wave speed. Make sure to pay attention to units and use the appropriate formula for the given units (e.g. meters for wavelength and hertz for frequency).

3. What is maximum displacement in relation to the wave speed equation?

Maximum displacement is the maximum distance that a particle in a wave moves from its rest position. It is often represented as A in the equation for wave motion, y = Asin(ωt + φ), where y is the displacement, ω is the angular frequency, t is time, and φ is the phase angle.

4. How do you calculate maximum displacement with a given wave speed?

To calculate maximum displacement with a given wave speed, you can use the equation A = v/ω, where A is the maximum displacement, v is the wave speed, and ω is the angular frequency. This equation assumes a sinusoidal wave with no phase shift. If there is a phase shift, the equation becomes A = v/ω * cos(φ).

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

Yes, the wave speed equation can be used for all types of waves, including mechanical waves (such as sound waves and water waves) and electromagnetic waves (such as light and radio waves). However, it is important to note that the equation may differ slightly for different types of waves, as some waves may have different properties that affect their speed.

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