Answer to Question #145587 in Optics for Daniel Divine Chinonso

Question

2 a place progressives' has the following equation y=5 sin (100fy t_0.4x) calculate (1)amplitude (2)angular velocity (3)wave length (4)frequency and period (5)linear velocity

Answer 1

solution

given equation

equation y=5 sin (100fy t_0.4x) comparing with standard equation

y=y₀sin ($\omega$ t-k x)

so

1)amplitude is y₀=5m

2)angular velocity $\omega=100\times 3.14=314rad/sec$

3)wavelength

$\lambda=\frac{2\pi}{k}=\frac{2\times3.14}{0.4}=15.7m$

4)frequency

$\omega=2\pi f$

$f=\frac{\omega}{2\pi}=\frac{100\pi}{2\pi}=50Hz$

period $T=\frac{1}{f}==\frac{1}{50}=0.02 sec$

5)linear velocity

$v=r\omega=y_0\omega=5\times100\times3.14=1570m/s$