Question

A progressive wave is given by $y=[3sin2\pi \left(\frac{t}{0.04}\right)-\left(\frac{x}{0.01}\right)]$ where x, y are in cm and t in s. The frequency of wave and maximum acceleration will be:

• A. $100Hz,4.7\times {10}^{3}m/s^2$
• B. $50Hz,7.5\times {10}^{3}m/s^2$
• C. $25Hz,4.7\times {10}^{4}m/s^2$
• D. $25Hz,7.5\times {10}^{4}m/s^2$

Answer 1

The correct option is D $25Hz,7.5\times {10}^{4}m/s^2$

$Weknown\omega =2\pi f=\frac{2\pi }{0.04}\Rightarrow f=25Hz$
Differentiating y.w.t. twice, we have
$y^{\prime \prime }=\frac{3\times 4{\pi }^2}{(0.004{)}^2}sin[\left(\frac{t}{0.04}\right)-\left(\frac{x}{0.01}\right)]$
For maximum acceleration
$y_0^{\prime \prime }=\frac{3\times 4{\pi }^2}{(0.004{)}^2}=7.5\times {10}^{4}m/s^2$