Wave function - displacement - transverse wave

  • #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
 

Answers and Replies

  • #2
Orodruin
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
Gold Member
16,829
6,652
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?

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
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
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
35,535
6,431
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.
 

Related Threads on Wave function - displacement - transverse wave

Replies
3
Views
1K
Replies
0
Views
2K
  • Last Post
Replies
1
Views
3K
Replies
2
Views
3K
  • Last Post
Replies
3
Views
16K
  • Last Post
Replies
8
Views
962
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
6
Views
4K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
5
Views
2K
Top