Question 267: Waves

Question

The equation of a progressive wave is $\mathrm{Y}=3 \sin \left[\pi\left(\frac{\mathrm{t}}{3}-\frac{\mathrm{x}}{5}\right)+\frac{\pi}{4}\right]$ where x and y are in meter and time in second. Which of the following is correct?

Accepted Answer

The general wave equation is:
$$ Y=A \sin (\omega t-k x+\phi) $$
Compare given wave equation with general wave equation,
$$ A=3 m ; \omega=\frac{\pi}{3} ; k=\frac{\pi}{5} ; \phi=\frac{\pi}{4} $$
Wavelength:
$$ \begin{array}{ll}  & \mathrm{k}=\frac{2 \pi}{\lambda} \Rightarrow \lambda=\frac{2 \pi}{\mathrm{k}} \Rightarrow \lambda=\frac{2 \pi}{\frac{\pi}{5}} \ 	herefore & \lambda=10 \mathrm{~m} \ & 	ext { Frequency: } \omega=2 \pi \mathrm{f}=\frac{\pi}{3} \Rightarrow \mathrm{f}=\frac{1}{6} \mathrm{~Hz} \ 	herefore & \mathrm{f}=\frac{1}{6} \mathrm{~Hz} \end{array} $$
Velocity: $v=\frac{\omega}{k}=\frac{\frac{\pi}{3}}{\frac{\pi}{5}} \Rightarrow v=\frac{5}{3} m / s$
$$ 	herefore \quad v=1.67 \mathrm{~m} / \mathrm{s} $$
Amplitude: $\mathrm{A}=3 \mathrm{~m}$

Answer

Wavelength $=10 \mathrm{~m}$

Answer

Velocity $=1.5 \mathrm{~m} / \mathrm{s}$

Answer

Amplitude $=3 \mathrm{~cm}$

Answer

Frequency $=0.2 \mathrm{~Hz}$

Waves

The equation of a progressive wave is \mathrm{Y}=3 \sin \left[\pi\left(\frac{\mathrm{t}}{3}-\frac{\mathrm{x}}{5}\right)+\frac{\pi}{4}\right] where x and y are in meter and time in second. Which of the following is correct?

Choose the correct answer: