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?

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 = ?

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

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.