### Step 1: Understanding the Problem You are asked to find the **multipole (\(\ell\))** the **four overtone** in a universe where the sound speed is \(c/\sqrt{2}\). You're told that multipoles are related to angular scales \(\theta\) (in radians) by: \[ \ell \approx \pi / \theta \] and the fundamental value is given as \(\ell = 5.2\). **Explanation:** The "fourth overtone" means the 5th peak (\(n = 5\)) since the fundamental is the first peak (\(n = 1\)), and overtones are counted from zero. Overtone \(m\) occurs at \(n = m+1\). --- ### Step 2: Calculating the Multipole for the Fourth Overtone If the first peak (fundamental) is at \(\ell_1 = 5.2\), the fourth overtone is the 5th peak: \[ \ell_5 = 5 \times \ell_1 = 5 \times 5.2 = 26 \] **Explanation:** Since the peaks are at integer multiples of the fundamental, the 5th peak is at \(5 \times\) the fundamental value. --- ### Final Answer **The approximate multipole for the fourth overtone is \(\boxed{26}\).**