How to Find Instantaneous Displacement in a Sinusoidal Wave?

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Homework Help Overview

The discussion revolves around determining the instantaneous displacement of a sinusoidal sound wave described by a specific wave function. The context involves applying the wave function to find displacement at a given position and time.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the correctness of substitutions made in the wave function. There is a focus on the calculation of the cosine value after simplifying the argument of the cosine function.

Discussion Status

Some participants have provided guidance on the calculation process, specifically regarding the mode of the calculator and the conversion of radians to degrees. Multiple interpretations of the calculations are being explored, but there is no explicit consensus on the final displacement value.

Contextual Notes

There is an emphasis on ensuring the correct mode for calculations and the potential confusion surrounding the conversion of radians and degrees. The original poster questions the correctness of their approach, indicating uncertainty in the process.

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Homework Statement



A sinusoidal sound wave is described by the displacement wave function
Code:
s(x,t)=(2.00 μm)cos⁡[(15.7 m^(-1) )x-(858 s^(-1) )t]
b) Determine the instantaneous displacement from equilibrium of the elements of air at the position x = 0.050 m at t = 3.00 ms

Homework Equations





The Attempt at a Solution


Code:
s (x,t)=(2.00 μm)  cos⁡[(15.7 m^(-1) )(0.050m)-(858 s^(-1) )(.003 s) ]

Why is this this not correct?
 
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Your substitutions are correct.
What is s = ?
 
s = 3ms
the answer is supposed to be -.433 μm
 
When you simplify the terms inside the bracket, you get 1.789 rad. To find the cos of this, either change the mode in your calculator to RAD or convert 1.789 rad to degrees and then solve for s.
 

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