Wave function - displacement - transverse wave

In summary, the transverse traveling wave on a string starts at x = 0 and travels towards x = ∞. The wave has an amplitude of 1.20 m, wavelength of 4.60 m and travels at a speed of 14.3 m/s. At time t = 0.0 s the displacement at position x = 0.0 m is 1.20 m. The reflected wave has an amplitude of 0.495 m and a wavelength of 4.60 m. The transmitted wave has an amplitude of 0.51 m and a wavelength of 4.60 m.
  • #1

Homework Statement


A transverse traveling wave on a string starts at x = 0 and travels towards x = ∞. The wave has an amplitude of 1.20 m, wavelength of 4.60 m and travels at a speed of 14.3 m/s . At time t = 0.0 s the displacement at position x = 0.0 m is 1.20 m.
(b) Calculate the displacement at position x = 2.6 m when t = 8.60 s.

An identical wave is launched on a new string, whose mass per unit length doubles at some position x > 0.
(c) Determine wavefunctions for the reflected and transmitted waves. You do not need to consider their amplitudes.

Homework Equations


y(x,t)=Acos(kx-wt)

The Attempt at a Solution


I think since at x=0 and t=0 , the displacement is equal to 1.2m, then we need to use y(x,t)=Acos(kx-wt) not y(x,t)=Asin(kx-wt) please tell me if this is true.
I got an answer for the displacement y(x,t)=y(2.6,8.60)=0,495m, using this formula: y(x,t)=Acos(kx-wt) but I am not sure if this is true. Please tell me if I am wrong and what should I do to fix it.
I found out that f=3.11Hz w=19.54 rad/s k=1.36
 
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  • #2
Jozefin Gramatikova said:
y(x,t)=Acos(kx-wt) not y(x,t)=Asin(kx-wt) please tell me if this is true.
The general expression is ##y(x,t) = A \sin(kx - \omega t + \phi)##, where ##\phi## is a constant. You can fix this constant using your information. The equations you quote are special cases. Does your choice satisfy the special case?

Jozefin Gramatikova said:
I found out that f=3.11Hz w=19.54 rad/s k=1.36
How did you arrive at these conclusions? It helps us if you write out your argumentation and computations so that they can be checked. What relations did you use to arrive at these numbers?
 
  • #3
Orodruin said:
The general expression is ##y(x,t) = A \sin(kx - \omega t + \phi)##, where ##\phi## is a constant. You can fix this constant using your information. The equations you quote are special cases. Does your choice satisfy the special case?How did you arrive at these conclusions? It helps us if you write out your argumentation and computations so that they can be checked. What relations did you use to arrive at these numbers?
f=v/lamda=14.3/4.6=3.11 Hz
w=2pif=2pi3.11=19.54 rad/s
k=2pi/lamda=2pi/4.6=1.36

this is given:
A=1.20 m
t= 8.60 s
x = 2.6

y(x,t)=Acos(kx-wt)
y(x,t)=1.2cos(1.36x2.6-19.64x8.6)
y(x,t)=1.2(-0.42)
y(x,t)=-0.51m

i think i was wrong with my previous result, but I am still unsure with the one that I got now
 
  • #4
Jozefin Gramatikova said:
y(x,t)=1.2cos(1.36x2.6-19.64x8.6)
Need to be careful with the precision here. If you have an expression like cos(2πa) then the integer part of a is irrelevant. If you have calculated a to three significant figures as -26.3 then you really only have one significant figure, -.3.
Try avoiding plugging in numbers so soon. (That's a good approach for many reasons.). Use symbols for all the given data, t for time, v for speed etc. You should get an expression of the form cos(2π(..)). Make sure you then calculate the ... part to three decimal places.
 

What is a wave function?

A wave function is a mathematical representation of a wave that describes the displacement of particles in a medium as the wave passes through it.

What is displacement in relation to waves?

Displacement is the distance that a wave has moved from its original position. It is measured as the distance between the crest (highest point) and the equilibrium position of the wave.

What is a transverse wave?

A transverse wave is a type of wave in which the particles of the medium move perpendicular to the direction of the wave. Examples of transverse waves include electromagnetic waves, such as light, and seismic S waves.

How is displacement related to the amplitude of a transverse wave?

The amplitude of a transverse wave is directly related to the displacement of the particles in the medium. A larger amplitude corresponds to a larger displacement, while a smaller amplitude corresponds to a smaller displacement.

What factors affect the displacement of a transverse wave?

The displacement of a transverse wave is affected by the amplitude, wavelength, and frequency of the wave. Additionally, the properties of the medium, such as its density and elasticity, can also affect the displacement of a transverse wave.

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