Solution (source code)

= Solution

Divide the physical sound radius by the <angular diameter distance> $a_*r_*$. The <sound-horizon angle in an open matter universe> is
$$
\boxed{\theta_s\simeq\sqrt{\frac{\Omega_ma_*}{3}}
=\frac{\sqrt{\Omega_m}}{60}\ \mathrm{rad}
\simeq0.955^\circ\sqrt{\Omega_m}.}
$$
The characteristic acoustic multipole is approximately half a wavelength across this angle:
$$
\boxed{\ell_s\sim\frac\pi{\theta_s}\simeq\frac{190}{\sqrt{\Omega_m}}.}
$$
Thus negative curvature moves the acoustic feature to smaller angular scales and larger multipoles. The first temperature peak is of order $200/\sqrt{\Omega_m}$ in this approximation; precise peak positions include the sound-speed history, radiation effects and acoustic phase shifts, so the acoustic-scale multipole is not an exact peak-location formula.