The longitudinal displacement of sound wave

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SUMMARY

The longitudinal displacement of a mass element in a medium as a sound wave passes through it is defined by the equation s = sm cos(kx – ωt). In this discussion, a sound wave with a frequency of 330 Hz and a wavelength of 0.95 m is analyzed, resulting in k = 6.6138 m-1 and ω = 2073.45 rad/s. The calculated displacement at x = 1.1 m and t = 0.12 s is s = -7.625 µm, which is incorrect due to a misunderstanding of the argument's units in the cosine function, which must be in radians.

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Homework Statement



The longitudinal displacement of a mass element in a medium as a sound wave passes through it is given by s = sm cos (kx – ωt). Consider a sound wave of frequency 330 Hz and wavelength 0.95 m. If sm= 16 µm, what is the displacement of an element of air located at x = 1.1 m at time t = 0.12 s?

Homework Equations


k=2π/λ
ω=2πƒ
ƒ≡ frequency
ω≡ angular frequency
λ≡ wavelength
k≡ angular wave number

The Attempt at a Solution


substitute the values of λ and f in k and ω to get k=6.6138 m^-1 and ω=2073.45
∴ s= 16 cos ( 6.6138*1.1-2073.45*0.12)=-7.625 INCORRECT
Where I made mistake?
 
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The argument of the cosine function is in what units? Radians or degrees?
 

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