Math Problem Statement
A sonar echo returns to a submarine 0.6 s after being emitted. What is the distance to the object creating the echo? (Assume that the submarine is in the ocean, and the speed of sound in ocean water is 1540 m/s).
Express the numeral of your answer in SI units with 3 or more significant figures.
Solution
To calculate the distance to the object, we use the formula:
The total distance traveled by the sound is given by:
Given:
- Speed of sound,
- Time for the echo to return,
Step 1: Calculate the total distance traveled by sound
Step 2: Calculate the one-way distance
Since the sound wave travels to the object and back, we divide the total distance by 2:
Final Answer:
The distance to the object is 462 m.
Would you like a detailed explanation or further assistance?
Related Questions:
- How is the speed of sound affected by water temperature?
- What factors can alter the accuracy of sonar measurements in real-world scenarios?
- How does sonar differ from radar in terms of propagation speed?
- What applications rely on sonar technology for distance measurement?
- How do salinity and pressure influence the speed of sound in seawater?
Tip:
Always account for environmental variables like temperature, salinity, and pressure, as they significantly affect sound speed in water.
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Math Problem Analysis
Mathematical Concepts
Distance calculation
Sound wave physics
Basic arithmetic operations
Formulas
Distance = Speed × Time
Distance to object = Total distance traveled by sound ÷ 2
Theorems
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Suitable Grade Level
Grades 6-8
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