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 2.60 s for the boat to travel from its highest point to its lowest, a total distance of 0.630 m. The fisherman sees that the wave crests are spaced a horizontal distance of 5.50 m apart.
How much is the wavelength?

Answer 1

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

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 2.60 s for the boat to travel from its highest point to its lowest, a total distance of 0.630 m. The fisherman sees that the wave crests are spaced a horizontal distance of 5.50 m apart.

How much is the wavelength?

How fast are the waves traveling ?

What is the amplitude A of wave?

Given Information:

time = t = 2.60 s

wavelength = λ  = 5.50 m

distance = d = 0.630 m

Required Information:

a)  wavelength = λ  = ?

b) speed = v = ?

c) Amplitude = A = ?

Answer:

a)  wavelength = 5.50 m

b) speed = 1.056 m/s

c) Amplitude = 0.315 m

Step-by-step explanation:

a)

It is given that wave crests are spaced a horizontal distance of 5.50 m apart that is basically the wavelength so,

λ  = 5.50 m

b)

We know that the speed of the wave is given by

v = λf

where λ is the wavelength and f is the frequency of the wave given by

f = 1/T

Where T is the period of the wave.

Since the it is given that boat takes 2.60 s to travel from its highest point to its lowest that is basically half of the period so one full period is

T = 2*2.60

T = 5.2 s

So the frequency is,

f = 1/5.2

f = 0.192 Hz

Therefore, the speed is

v = λf

v = 5.50*0.192

v = 1.056 m/s

c)

The amplitude of the wave is given by

A = d/2

where d is the distance from the highest point to the lowest, therefore, the amplitude is half of it.

A = 0.630/2

A = 0.315 m