(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A travelling sound wave causes a variation in air pressure according to the equation:

∆P = 20.0 sin(15.5x − 5.32 × 10^{3}t )

where x is in metres, t in seconds and pressure is in pascals.

What is the amplitude of the displacement of the air particles caused by this pressure wave (i.e. the displacement amplitude)?

Take ρ_{air}=1.21 kgm^{–3}.

2. Relevant equations

Pressure amplitude is related to displacement amplitude by

[tex]\Delta P_{max}= \rho v \omega s_{max}[/tex]

3. The attempt at a solution

I know that the angular frequency ω of the pressure wave is 5320.0 rads^{–1}, and the velocity v of the pressure wave is 343.0 ms^{–1}. But I can't use the formula above because I can't determine the value of [tex]\Delta P_{max}[/tex].

How can I find [tex]\Delta P_{max}[/tex] from

∆P = 20.0 sin(15.5x − 5.32 × 10^{3}t )

when I don't know the values of "x" and "t"? What values do I need to substitute there?

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# Homework Help: Displacement amplitude

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