Question

A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes 2.5 s for the boat to travel from its highest point to its lowest, a total distance of 0.62 m. The fisherman sees that the wave crests are spaced 6.0 m apart. (a) How fast are the waves traveling? (b) What is the amplitude of each wave? (c) If the total vertical distance traveled by the boat were 0.30 m but the other data remained the same, how would the answers to parts (a) and (b) be affected?

Answer 1

Answer:

1.2 m/s

0.31 m

0.15 m

Explanation:

Time period is

$T=2.5\times 2\\\Rightarrow T=5\ s$

Frequency is

$f=\dfrac{1}{T}\\\Rightarrow f=\dfrac{1}{5}\\\Rightarrow f=0.2\ Hz$

Velocity is given by

$v=f\lambda\\\Rightarrow v=0.2\times 6\\\Rightarrow v=1.2\ m/s$

The waves are traveling at 1.2 m/s

Amplitude is given by

$A=\dfrac{d}{2}\\\Rightarrow A=\dfrac{0.62}{2}\\\Rightarrow A=0.31\ m$

Amplitude is 0.31 m

If d = 0.3 m

$A=\dfrac{0.3}{2}=0.15\ m$

The amplitude would be 0.15 m. The speed would remain the same.