Question

Answer question 2!!

1. a boat is bobbing up and down on the water as waves pass underneath it. The depth of the water under the boat oscillates between 3 m and 4 m. The boat is stationary with respect to the shore and it is 2.9s between the crests of successive waves. A person on shore sees the crests of the wave passing by at 2 m/s. what is the distance between crests of this wave?

2. Two ducks are floating close together on the water near the boat in problem 1. When the first duck is on the peak of a passing wave the second duck is 30 cm below it and moving upwards. How far apart are the ducks?

Answer 1

Solution:

The vertical distance between the waves = 30 cm = 0.30 m

The time period = T = 2.9s

Angular Velocity of the wave = = 2 pi/T = 2 pi/2.9 = 2.17 rad/s

general wave form: y= A cos t

0.30 = 0.5 cos (2.17t) =>cos(2.17 t) = 0.3/0.5 =0.6

=>2.17t = cos^-1(0.6) =53.1 degrees = 0.927 radians

=> t = 0.927/2.17 = 0.427 s, at this time , the duck is headed down the peak.

So the other position is chosen for the duck's placement at a later time , which is calculated as follows:

and 2pi -0.927 = 5.36rad

t=5.36/2.17 =2.47 s

v=frequency x wavelength = (1/2.9)(wavelength)

=>wavelength =v/frequency = 2/0.34 = 5.88 m

The distance between the ducks = X (along the horizontal) = t/T *(wavelength)

                                                            = ( 2.47)*(5.88)/2.9 = 5 m