Calculating Displacement with Sine Waves

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SUMMARY

The discussion centers on calculating displacement using the sine wave equation y=0.2msin[(0.18rad/m)x+(90 rad/s)t - pi/4]. The correct displacement at position x=0 and time t=0 is determined to be -0.141m, as derived from the sine function. Participants emphasize the importance of using radians instead of degrees and correctly applying the sine function, particularly noting that sin(-pi/4) equals -0.707. Miscalculations arose from incorrect arithmetic and misunderstanding of the sine function's output at specific angles.

PREREQUISITES
  • Understanding of wave equations, specifically y(x,t)=Asin(kx-wt+phi)
  • Knowledge of trigonometric functions, particularly sine and its properties
  • Familiarity with radians and degrees in mathematical calculations
  • Basic algebra for manipulating equations and solving for variables
NEXT STEPS
  • Review the properties of the sine function, especially sin(-pi/4)
  • Practice converting between radians and degrees in trigonometric calculations
  • Explore wave mechanics and the significance of amplitude, wavelength, and phase
  • Learn about common mistakes in trigonometric calculations and how to avoid them
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Students studying physics or mathematics, particularly those focusing on wave mechanics and trigonometry, as well as educators looking to clarify common misconceptions in these areas.

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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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