Find Range of Ray Emitted Horizontally at Depth 150m in Water

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In summary, the conversation discussed calculating the range at which a horizontally emitted sound ray at a depth of 150m will reach the surface, given the speed of sound in water at the surface (1600m/s) and its linear increase with depth (0.017/s). The relevant equation used was the radius of curvature of the ray (R = c0/g) and the resulting answer was 4200m. However, the speaker was unsure of how their teacher arrived at this answer and questioned if any information was missing. The correct formula for calculating the horizontal range was also provided as x = sqrt( (2*c*d) / g)).
  • #1
yemmdizzle006
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Homework Statement


speed of sound in water is 1600m/s at the surface and increases linearly with depth at a rate of 0.017/s, find the range at which a ray emitted horizontally at a source of dept 150m will reach the surface


C = sound speed in water (1500m/s)

gradient = g (0.017/s)

Homework Equations



Relevant equations I used will be calculate the Radius of the curvature of the Ray

R (curvature of Ray) = c0/g


The Attempt at a Solution



I keep getting a huge figure 883880m ...

and i know it is not correct.
 
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  • #2
apparently the answer is that at 4200m, the ray emitted horizontally will reach the surface.I have no idea how my teacher came up with that.Is there some piece of information I am missing?
 
  • #3
solution

x = horizontal range

c = speed of sound

d = depth

g = gradient

x = sqrt( (2*c*d) / g))

Thank you!
 

1. What is the speed of light in water at a depth of 150m?

The speed of light in water at a depth of 150m is approximately 1,458 meters per second. This is about 75% of the speed of light in a vacuum, which is 299,792,458 meters per second.

2. How is the range of a ray emitted horizontally at depth 150m in water calculated?

The range of a ray emitted horizontally at depth 150m in water is calculated using the equation:
range = (speed of light in water) x (time taken for ray to travel)
Since the ray is emitted horizontally, the time taken for it to travel is equal to the distance it travels divided by the speed of light in water. This gives us the equation:
range = (speed of light in water)^2 x (depth of water) / (speed of light in water)

3. How does the depth of water affect the range of a horizontally emitted ray in water?

The depth of water has a direct effect on the range of a horizontally emitted ray in water. As the depth increases, the range also increases. This is because the time taken for the ray to travel increases with depth, and thus the range also increases according to the equation mentioned in the previous answer.

4. What factors can affect the accuracy of calculating the range of a ray emitted horizontally at depth 150m in water?

Some factors that can affect the accuracy of calculating the range of a ray emitted horizontally at depth 150m in water include the accuracy of the speed of light in water at that depth, the accuracy of the time measurement, and any external factors that may interfere with the ray's path, such as impurities or objects in the water.

5. How is the speed of light in water at a depth of 150m measured?

The speed of light in water at a depth of 150m can be measured using various methods, such as time-of-flight measurements or interferometry. These methods involve sending a light pulse through the water at the desired depth and measuring the time it takes to travel a known distance. This time is then used to calculate the speed of light in water at that depth.

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