What is the frequency of the wave?

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SUMMARY

The frequency of a sound wave traveling at 345 m/s through air can be determined using the wave equation s = sm cos(kx - ωt + φ). Given that the maximum displacement (sm) is 6.30 nm at x = 2.00 m and 2.40 nm at x = 2.09 m, the wave's properties can be analyzed. The phase relationship between the displacements indicates that the wave is periodic and can be further explored using the wave's angular frequency (ω) and wave number (k). The discussion clarifies the need to apply inverse trigonometric functions to find specific values related to the wave's characteristics.

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FearlessRose
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A sound wave of the form s = sm cos(kx - ωt + φ) travels at 345 m/s through air in a long horizontal tube. At one instant, air molecule A at x = 2.00 m is at its maximum positive displacement of 6.30 nm and air molecule B at x = 2.09 m is at a positive displacement of 2.40 nm. All the molecules between A and B are at intermediate displacements. What is the frequency of the wave?
Here is what I've gotten so far.
s=6.30 nm at 2m
s=240nm at 2.09
since s is max at 2m, the sm=6.40nm

s=smcos(kx-wt+phi)
kx-wt + phi=acos(s/sm)

I have everything I need but, how do I find out what the value of a is?
 
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There is no a, acos stands for arccos(y), the inverse cosine function.
 
Thank you!
 

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