  We present a way to search for light scalar dark matter (DM), seeking to
exploit putative coupling between dark matter scalar fields and fundamental
constants, by searching for frequency modulations in direct comparisons between
frequency stable oscillators. Specifically we compare a Cryogenic Sapphire
Oscillator (CSO), Hydrogen Maser (HM) atomic oscillator and a bulk acoustic
wave quartz oscillator (OCXO). This work includes the first calculation of the
dependence of acoustic oscillators on variations of the fundamental constants,
and demonstration that they can be a sensitive tool for scalar DM experiments.
Results are presented based on 16 days of data in comparisons between the HM
and OCXO, and 2 days of comparison between the OCXO and CSO. No evidence of
oscillating fundamental constants consistent with a coupling to scalar dark
matter is found, and instead limits on the strength of these couplings as a
function of the dark matter mass are determined. We constrain the dimensionless
coupling constant $d_e$ and combination $|d_{m_e}-d_g|$ across the mass band
$4.4\times10^{-19}\lesssim m_\varphi \lesssim 6.8\times10^{-14}\:\text{eV}
c^{-2}$, with most sensitive limits $d_e\gtrsim1.59\times10^{-1}$,
$|d_{m_e}-dg|\gtrsim6.97\times10^{-1}$. Notably, these limits do not rely on
Maximum Reach Analysis (MRA), instead employing the more general coefficient
separation technique. This experiment paves the way for future, highly
sensitive experiments based on state-of-the-art acoustic oscillators, and we
show that these limits can be competitive with the best current MRA-based
exclusion limits.
