Solving the Mystery Problem: Finding the Submarine Depth & Velocity

[motherlovebone]

Okay, I need some help yet again. Our teacher is giving us no hints on the "mystery problem" on our test tomorrow.

"A boat sends a sonar down to find a submarine underwater. The boat estimates the velocity of sound under the water to be 1500 m/s. Howeer, they are wrong about that velocity. Find their mistake, explain it, and then find how deep the submarine is in the water and find the real velocity of sound under the water."

 

[vaishakh]

The given information proves to be insufficient. The problem must be that the sonar instrument need not have been kept vertical.

 

[kyle8921]

I understand the importance of accuracy and precision in measurements. In this scenario, it is clear that the boat has made a mistake in estimating the velocity of sound under the water to be 1500 m/s. This mistake could have occurred due to various factors such as human error, equipment malfunction, or incorrect calibration.

To solve this mystery problem, the first step would be to identify the actual velocity of sound under the water. This can be done by conducting experiments and collecting data from various sources. Once the correct velocity is determined, it can be compared to the boat's estimated velocity to determine the magnitude of the error.

To explain this mistake, it is important to understand the factors that affect the velocity of sound in water. Some of these factors include temperature, salinity, and pressure. Changes in these variables can significantly impact the velocity of sound, leading to inaccurate estimations.

In order to find the depth of the submarine, we can use the equation v = d/t, where v is the velocity of sound, d is the depth, and t is the time taken for the sound to travel from the boat to the submarine and back. By rearranging this equation, we can solve for d and determine the actual depth of the submarine.

Furthermore, to find the real velocity of sound under the water, we can use the formula v = d/t, where d is the distance between two points on the surface of the water and t is the time taken for sound to travel between those points. By measuring the distance and time accurately, we can calculate the real velocity of sound under the water.

In conclusion, the mistake made by the boat in estimating the velocity of sound under the water can be rectified by conducting experiments and collecting accurate data. By understanding the various factors that affect the velocity of sound and using relevant equations, we can determine the correct velocity and depth of the submarine.