JEE Main Physics: Beats from cos A cos B Form 💡
❓ Question Two harmonic waves moving in the same direction superimpose to form a wave: x = a cos ( 1.5 t ) cos ( 50.5 t ) x = a \cos(1.5t)\cos(50.5t) (where t t is in seconds) Find the period with which they beat . (Answer close to nearest integer) 🖼️ Question Image ✍️ Short Solution This is a standard beats question hidden inside a product form. Key idea: 👉 Product of cosines = amplitude modulation 🔥 🎯 HOOK (Before Reading) “Wave ke andar wave dikhe? Samajh jao beats chal rahe hain!” 🎵 🔹 Step 1 — Identify the Structure (MOST IMPORTANT 💯)** Given: x = a cos ( 1.5 t ) cos ( 50.5 t ) x = a \cos(1.5t)\cos(50.5t) x = a cos ( 1.5 t ) cos ( 50.5 t ) This is of the form: x = ( slow term ) × ( fast term ) x = (\text{slow term}) \times (\text{fast term}) x = ( slow term ) × ( fast term ) Here: cos ( 50.5 t ) \cos(50.5t) cos ( 50.5 t ) → rapid oscillation cos ( 1.5 t ) \cos(1.5t) cos ( 1.5 t ) → slowly varying...