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irina [24]
3 years ago
5

A fisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surfac

e 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?
Physics
1 answer:
frutty [35]3 years ago
8 0

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

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Answer:

θ = 30°

Explanation:

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n_{1}sin(\theta_{1}) = n_{2}sin(\theeta_{2})

<u>Where</u>:

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Hence, θ₂ is:

sin(\theta_{2}) = \frac{n_{1}*sin(\theta_{1})}{n_{2}} = \frac{1*sin(30)}{1.46} = 0.34 \rightarrow \theta_{2} = 20.03 ^{\circ}

Now, when the beam of light re-emerges from the opposite side, we have:

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n₂: is the medium 2 (air) = 1

θ₂: is the transmission angle

Hence, the angle to the normal to that surface (θ₂) is:

sin(\theta_{2}) = \frac{n_{1}*sin(\theta_{1})}{n_{2}} = \frac{1.46*sin(20.03)}{1} = 0.50 \rightarrow \theta_{2} = 30 ^{\circ}  

 

Therefore, we have that the beam of light will come out at the same angle of when it went in, since, it goes from air and enters to a plastic medium and then enters again in this medium to go out to air again. This was proved using the Snell Law.    

I hope it helps you!                

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solution

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see attachment

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