Calculating Displacement with Sine Waves

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Homework Help Overview

The discussion revolves around calculating displacement using a sine wave equation, specifically analyzing the function y=0.2msin[(0.18rad/m)x+(90 rad/s)t - pi/4] at the initial conditions of x=0 and t=0.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the calculation of displacement by substituting values into the sine wave equation, questioning the origin of certain values and the correctness of their calculations. There are discussions about the sine function's behavior at specific angles and the importance of using the correct mode (radians vs degrees).

Discussion Status

There is an ongoing exploration of the calculations, with some participants expressing confusion over the results and others attempting to clarify the steps involved. A few participants have provided insights into the sine function's output at specific angles, but no consensus has been reached on the correct displacement value.

Contextual Notes

Participants are grappling with the implications of phase shifts in the sine function and the potential for errors in calculation, particularly regarding the use of radians and the interpretation of the sine of negative angles.

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Homework Statement



y=0.2msin[(0.18rad/m)x+(90 rad/s)t - pi/4]

What is the displacement at position x=0 and t=0?

Homework Equations



y(x,t)=Asin(kx-wt+phi)

The Attempt at a Solution



y=0.2m[0.18-90]=-0.199m

the answer is -.141 m help?
 
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ScienceGeek24 said:
y=0.2m[0.18-90]=-0.199m
Where did the 0.18 come from? x = 0.

And don't mix radians and degrees. And don't forget the sine.
 
Last edited:
As the above post said, the displacement is 0. This is because at x=0, t= 0, so everything in the sin function becomes 0. Sin of 0 is 0. Hence the displacement =0
 
the displacement can't be 0 because the answer sheet says is -.141m and when i put x=0 i still get the same asnwer -0.199m don't get it.
 
The value of x is 0, not the displacement (which is the y value).
ScienceGeek24 said:
and when i put x=0 i still get the same asnwer -0.199m don't get it.
Show exactly what you did.
 
Silly me, forgot the phase of the thing. Since everything else in the sin =0, then sin(-pi/4) =-1/(sqrt(2) multiply this by 0.2 and you get your answer of -0.141m.
 
Never mind what i was doing was wrong i was subtracting .18-90 and the sine of that time 0.2m is .199m

but what hypnosam is doing seems right

I did y= 0.2sin[0.18(0)+90(0)-pi/4] but i just don't know how he got 0.707 when inmy calculator i get 0.013 for sin(-pi/4) wth.
 
ScienceGeek24 said:
I did y= 0.2sin[0.18(0)+90(0)-pi/4] but i just don't know how he got 0.707 when inmy calculator i get 0.013 for sin(-pi/4) wth.
Make sure you're using radian mode.
 
got it thanks!
 

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