Find Displacement Amplitude for 79.8dB Wave

AI Thread Summary
The discussion centers on calculating the displacement amplitude of a sound wave at a level of 79.8 dB, specifically for a note with a wavelength of 0.232m. The relevant equations involve pressure amplitude, frequency, and speed of sound, but the user struggles to find the necessary equation for pressure amplitude (Δpo). They suspect that loudness is related to this calculation but have not found a solution after extensive searching. The conversation highlights the challenge of linking sound pressure levels to displacement amplitude in acoustic physics. Overall, the user seeks assistance in resolving the calculation for displacement amplitude based on the given parameters.
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The highest note written for a singer in a published score was F-sharp above high C, 1.48 kHz, for Zerbinetta in the original version of Richard Strauss's opera Ariadne auf Naxos.
The wavelength of this wave is 0.232m.
Suppose people in the fourth row of seats hear this note with level 79.8 dB. Find the displacement amplitude of the sound.


A=Δpo/ωρc
f=v/λ
ω=2∏f

By substituting all the known values into the first equation I'm left with an unknown variable - Δpo.

I've looked everywhere to try and discover an equation for the pressure amplitude but to no avail. I'm assuming it has something to do with the loudness I've been given but I've been plugging away for an hour or so now and I've come nowhere near a correct answer.
 
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