Question

A fisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surface of the water. It takes a time of 2.90 s for the boat to travel from its highest point to its lowest, a total distance of 0.700 m . The fisherman sees that the wave crests are spaced a horizontal distance of 5.50 m apart.
How fast are the waves traveling?


What is the amplitude A of each wave?

Answer 1

Answer:

Velocity=1.1m/s

Amplitude=0.35m

Explanation:

Given:

time 't' = 2.9s

wavelength 'λ'= 5.5m

distance 'd'=0.7m

The time period 't' is the time b/w two successive waves. Therefore, the time it takes from the boat to travel  from its highest point to its lowest is a half period.

So, T = 2 x 2.9 => 5.8 s

As we know that frequency is the reciprocal of time period, we have

f= 1/T = 1/5.8 =>0.2 Hz

In order to find how fast are the waves traveling, the velocity is given by

Velocity = f λ

V= 0.2 x 5.5 =>1.1m/s

The distance between the boat's highest point to its lowest point is double the amplitude.

Therefore , we can write

Amplitude 'A'= d/2 =>0.7/2 =>0.35m