Two vibrating tuning forks produce waves given by $y_{1}=A \cos (1000 \pi t)$ and $y_{2}=A \cos (100

Question

Two vibrating tuning forks produce waves given by $y_{1}=A \cos (1000 \pi t)$ and $y_{2}=A \cos (1008 \pi t)$. The number of beats heard per second is

Professor PC Thomas Classes · Answer

(a) : Comparing the given wave equations with the standard equation $y = A \cos(\omega t)$, the angular frequencies are $\omega_1 = 1000\pi$ and $\omega_2 = 1008\pi$. The linear frequencies are $f_1 = \frac{\omega_1}{2\pi} = 500 \mathrm{~Hz}$ and $f_2 = \frac{\omega_2}{2\pi} = 504 \mathrm{~Hz}$. The number of beats produced per second is $|f_1 - f_2| = |500 - 504| = 4$.