A buoy, floating in a ripple tank, is at rest when a wave reaches it. The wave has a frequency of 1.25 Hz, and an amplitude of 0.75 m. What is the magnitude of the buoy’s displacement after 2.20 seconds?
Answers
Answer:
See Below
Explanation:
The magnitude of the buoy’s displacement after 2.20 seconds is \bold { -6.57 10^{-3\ } m}−6.5710
−3
m .
The movement of water is an oscillation in the vertical direction can be calculated by
\bold { y = A cos (\omega t)}y=Acos(ωt)
where,
A - amplitude = 0.75 m
\bold {\omega}ω - angular velocity
Relationship between angular velocity and frequency
\begin{gathered}\bold { \omega = 2\pi f}\\\\ \bold { \omega = 2\pi 1.25}\\\\\bold { \omega = 7.85\ rad / s}\end{gathered}
ω=2πf
ω=2π1.25
ω=7.85 rad/s
Now put the values,
\begin{gathered}\bold { y = 0.75 cos (7.85 \times 2.2)}\\\\ \bold {y = -0.00657\ m}\\\\ \bold { y = \bold { -6.57 10^{-3\ } m}}\end{gathered}
y=0.75cos(7.85×2.2)
y=−0.00657 m
y=−6.5710
−3
m
The magnitude of the buoy’s displacement after 2.20 seconds is \bold { -6.57 10^{-3\ } m}−6.5710
−3
m .