A sinusoidal sound wave is described by the displacement s(x, t) = s m cos(kx t)

Question

A sinusoidal sound wave is described by the displacement

s(x, t) = sm cos(kx t)

where sm = 4.08 m, k = 16.3 rad/m, and = 820 rad/s.

Determine the instantaneous displacement of the molecules at the position x = 0.0675 m at t = 4.07 ms. Answer in units of m.

I tried just plugging in all the formulas, but I believe my conversions are incorrect or my process as I'm not getting the right answer.

s(.0675, 5.07) = 4.08E-6 Cos ( 16.3(.0675) - 820(4.07) )

My two attempts at this problem :

Converting m 4.069532E-6

No Conversion 4.069532

Explanation / Answer

One issue I'm seeing here is that you're not converting the time units. ms implies miliseconds, which means you should be multiplying by .00407 seconds not 4.07 seconds. Here's my attempt for you: s(.0675,.00407) = 4.08E-6 * cos(16.3*(.0675)-820(0.00407)) = -2.521E-6 Hope this helps :)

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