Q. A wave is given by $y = 3\sin{2\pi}\left( \frac{t}{0.04} - \frac{x}{0.01} \right)$, where $y$ is in $cm$. Frequency of wave and maximum acceleration of particle will be
A) $100Hz,\ 4.7 \times 10^{3}cm/s^{2}$
B) $500Hz,\ 7.5 \times 10^{3}cm/s^{2}$
C) $25Hz,\ 4.7 \times 10^{4}cm/s^{2}$
D) $25Hz,\ 7.4 \times 10^{4}cm/s^{2}$
Explanation
(d) Comparing the given equation with standard equation
$y = a\sin{2\pi}\left( \frac{t}{T} - \frac{x}{\lambda} \right) \Rightarrow T = 0.04sec \Rightarrow v = \frac{1}{T} = 25Hz$
Also $(A)_{\max} = \omega^{2}a = \left( \frac{2\pi}{T} \right)^{2} \times a = \left( \frac{2\pi}{0.04} \right) \times 3$
$= 7.4 \times 10^{4}cm/\sec^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.