Two harmonic waves moving in the same direction superimpose to form a wave $x=a \cos (1.5 t) \cos (5

Question

Two harmonic waves moving in the same direction superimpose to form a wave $x=a \cos (1.5 t) \cos (50.5 t)$ where $t$ is in seconds. Find the period with which they beat. (close to nearest integer)\

Professor PC Thomas Classes · Answer

(a) : Given, that, $x=a \cos (1.5 t) \cos$\ ( $50.5 t$ )\ $x=\frac{a}{2} \cos (50.5 t+1.5 t)+\frac{a}{2} \cos (50.5 t-1.5 t)$\ $x=\frac{a}{2} \cos (52 t)+\frac{a}{2} \cos (49 t)$\ $F_{1}=\frac{52}{2 \pi}$ and $F_{2}=\frac{49}{2 \pi}$\ $	herefore \quad \Delta F=F_{1}-F_{2}=\frac{52}{2 \pi}-\frac{49}{2 \pi}=\frac{3}{2 \pi} \mathrm{~Hz}$\ $\Delta T=\frac{1}{\Delta F}=\frac{2 \pi}{3}=2.09 \simeq 2 \mathrm{~s}$