Answer
(a) It takes 1.01 seconds for one complete wave pattern to go past.
The wave crest travels a horizontal distance of 15.3 cm in a time of 1.01 seconds.
(b) The wave number is 0.410 rad/cm
The number of waves that pass each second is 0.987
(c) The speed of the wave crest is 15.1 cm/s
The maximum speed of the cork floater is 17.05 cm/s
Work Step by Step
We can write the general equation for a wave equation when the wave is moving in the negative x-direction.
$y(x,t) = A~cos(k~x+\omega~t)$
(a) We can find the period.
$T = \frac{2\pi}{\omega}$
$T = \frac{2\pi}{6.20~rad/s}$
$T = 1.01~s$
It takes 1.01 seconds for one complete wave pattern to go past.
We can find the wavelength.
$\lambda = \frac{2\pi}{k}$
$\lambda = \frac{2\pi}{0.410~rad/cm}$
$\lambda = 15.3~cm$
The wave crest travels a horizontal distance of 15.3 cm in a time of 1.01 seconds.
(b) The wave number is $k$ which is 0.410 rad/cm
We can find the frequency.
$f = \frac{\omega}{2\pi}$
$f = \frac{6.20~rad/s}{2\pi}$
$f = 0.987~Hz$
The number of waves that pass each second is 0.987
(c) We can find the speed of the wave crest.
$v = \lambda~f$
$v = (15.3~cm)(0.987~Hz)$
$v = 15.1~cm/s$
The speed of the wave crest is 15.1 cm/s
We can find the maximum speed of the cork floater.
$v_{max} = A~\omega$
$v_{max} = (2.75~cm)(6.20~rad/s)$
$v_{max} = 17.05~cm/s$
The maximum speed of the cork floater is 17.05 cm/s
