Ocean Depth at 7.07s Echo Time - 1.22311 km

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SUMMARY

The ocean depth at a point where the echo time is 7.07 seconds is calculated to be 1.22311 kilometers using the speed of sound in air. However, this calculation is incorrect as it does not account for the speed of sound in seawater, which is influenced by temperature, salinity, and pressure. The correct approach requires a more complex formula that incorporates these variables, as the speed of sound in seawater differs significantly from that in air.

PREREQUISITES
  • Understanding of sound wave propagation in different mediums
  • Knowledge of the speed of sound in seawater
  • Familiarity with the effects of temperature, salinity, and pressure on sound speed
  • Basic mathematical skills for calculating depth using echo time
NEXT STEPS
  • Research the speed of sound in seawater and its dependency on temperature, salinity, and pressure
  • Learn about the equations used to calculate sound speed in oceanographic contexts
  • Explore the impact of oceanographic variables on sonar technology
  • Investigate methods for measuring ocean depth using echo-sounding techniques
USEFUL FOR

Marine scientists, oceanographers, and anyone involved in underwater acoustics or sonar technology will benefit from this discussion.

mikefitz
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A geological survey ship mapping the floor of the ocean sends sound pulses down from the surface and measures the time taken for the echo to return. How deep is the ocean at a point where the echo time (down and back) is 7.07 s? The temperature of the seawater is 25°C. Find the answer in km

7.07 / 2 = 3.535 seconds to get from surface to ocean bedrock.
v = 331 + .6*25 = 346 m/s

3.535 * 346 = 1223.11 m ==> 1 223.11 meters = 1.22311 kilometers

This is wrong according to the online homework I'm doing?
 
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Perhaps you need the speed of sound in sea water instead of air?
 
Your math is correct as far as I can see. However... the equation you are using for the speed of sound is for air. It is different in water. The actual equation is very complex and dependent on salinity and pressure as well as temperture. You obviously were not given salinity and pressure varies with depth so maybe I am making this too complex. Ideas anyone?

Just for interest: Salinity changes in the oceans causes the sound to bend and reflect in an unpredictable manner. This allows subs to hide beneath various layers making sub hunting a very difficult problem.
 

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