Find Displacement Amplitude for 79.8dB Wave

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SUMMARY

The discussion focuses on calculating the displacement amplitude of a sound wave at a sound level of 79.8 dB, specifically for the F-sharp note at 1.48 kHz from Richard Strauss's opera Ariadne auf Naxos. The wavelength of the wave is given as 0.232m. The formula used for displacement amplitude is A=Δpo/ωρc, where Δpo is the pressure amplitude, ω is the angular frequency, and ρc is the product of density and speed of sound. The user struggles to find the equation for pressure amplitude related to loudness, indicating a gap in available resources for this specific calculation.

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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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