An acoustic beat produces a combined sound wave represented by the function $f(x)=\cos (2 \pi \cdot 41 x)+\cos (2 \pi \cdot 53 x)$.

Question

Quizplus · Accepted Answer

The sum of two cosine functions can be expressed using the product-to-sum identities: $\cos A + \cos B = 2 \cos \left(\frac{A+B}{2}\right) \cos \left(\frac{A-B}{2}\right)$. Here, $A = 2\pi \cdot 41x$ and $B = 2\pi \cdot 53x$, so the expression simplifies to $2 \cos (2 \pi \cdot 47 x) \cos (2 \pi \cdot 6 x)$.

An Acoustic Beat Produces a Combined Sound Wave Represented by the Function