Question 295: Waves

Question

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 the wave and maximum acceleration will be $\left(\pi^2=10\right)$

Accepted Answer

The wave equation is given by:
$ Y = 3 \sin 2\pi\left(\frac{t}{0.04} - \frac{x}{0.01}ight) $
where $ Y $ is in centimeters. To find the frequency and maximum acceleration, we can compare it to the standard wave equation:
$ y = A \sin 2\pi\left(ft \pm \frac{x}{\lambda}ight) $
From $ \frac{t}{0.04} = ft $, we find:
$ f = \frac{1}{0.04} = 25 \, 	ext{Hz} $
The angular frequency $ \omega $ is given by:
$ \omega = 2\pi f = \frac{2\pi}{0.04} $
To find the maximum acceleration $ a_{	ext{max}} $, we use:
$ a_{	ext{max}} = \omega^2 A $
Substituting the given values:
$ a_{	ext{max}} = \frac{4 	imes \pi^2 	imes 3}{(0.04)^2} $
Given $ \pi^2 = 10 $:
$ a_{	ext{max}} = \frac{4 	imes 10 	imes 3}{0.0016} $
$ = 7.5 	imes 10^4 \, 	ext{cm/s}^2 $
Therefore, the frequency of the wave is $ 25 \, 	ext{Hz} $ and the maximum acceleration is approximately $ 7.5 	imes 10^4 \, 	ext{cm/s}^2 $.

Answer

$100 \mathrm{~Hz}, 4.7 	imes 10^4 \mathrm{~cm} / \mathrm{s}^2$

Answer

$50 \mathrm{~Hz}, 7.5 	imes 10^3 \mathrm{~cm} / \mathrm{s}^2$

Answer

$25 \mathrm{~Hz}, 4.7 	imes 10^4 \mathrm{~cm} / \mathrm{s}^2$

Answer

$25 \mathrm{~Hz}, 7.5 	imes 10^4 \mathrm{~cm} / \mathrm{s}^2$

Waves

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 the wave and maximum acceleration will be \left(\pi^2=10\right)

Choose the correct answer: