An equation that explains the relationship between the sound strength and medium pressure I am doing an experiment that explores the correlation between sound strength and air pressure. Experimentally I got that by increasing the air pressure, the sound strength increases with it.
My question is the following: With which mathematical model can we calculate the sound strength in a set air pressure using the following: the air pressure around the sound source, the sound strength, and frequency of the sound source at standard conditions?
 A: A sound wave in a transmission medium causes a deviation (sound pressure $p$, a dynamic pressure) in the local ambient pressure, a static pressure, $p_{\textrm{stat}}$. In your case, the medium is air and the total pressure within the medium during transmission is given by $p_{\textrm{tot}} = p_{\textrm{stat}} + p$.
What you require for your analysis is the sound pressure $p$ (typically measurable with a microphone). The sound intensity or strength $\vec{I}$ is given by $p\vec{v}$, where $\vec{v}$ is the particle velocity in the medium. For a period of time $T$,
$$ \left\langle \vec{I} \right\rangle = \frac{1}{T} \int_{0}^{T} p(t) \vec{v}(t), $$
is called the average sound intensity. For a planar sound wave, one typically has,
$$ I = 2\pi^2 \xi^2 \nu^2 c \rho, $$
where, $\rho$ is the medium density, $\xi$ is the amplitude of the wave or particle displacement, $\nu$ is the frequency and $c$ is the speed of sound in the medium. The direction of sound intensity is the average direction in which energy is flowing. In other words, the sound intensity is directly proportional to the medium density and thus the medium pressure $(\rho \propto V^{-1} \propto P)$, which confirms your experimental result.
