A submarine sonar system sends a burst of sound with a frequency of

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SUMMARY

The submarine sonar system emits a sound burst at a frequency of 325Hz, which travels to an underwater rock face and returns in 8.50 seconds. The velocity of sound in water is calculated using the formula v=fλ, resulting in a speed of 1530.75 m/s. The distance to the rock face is determined by the formula d=vt, yielding a total distance of 13011.375 meters, which is halved for the round trip, resulting in a final distance of 6.51 kilometers. The key error identified was neglecting the round trip of the sound wave.

PREREQUISITES
  • Understanding of sound wave properties, including frequency and wavelength.
  • Familiarity with the speed of sound in water, specifically 1530.75 m/s.
  • Knowledge of basic physics formulas: v=fλ and d=vt.
  • Ability to interpret time and distance relationships in wave propagation.
NEXT STEPS
  • Study the principles of sonar technology and its applications in underwater navigation.
  • Learn about the effects of temperature and salinity on the speed of sound in water.
  • Explore advanced wave propagation concepts, including reflection and refraction of sound waves.
  • Investigate the mathematical modeling of sound waves in different mediums.
USEFUL FOR

Students in physics, marine engineers, and professionals working with sonar systems or underwater acoustics will benefit from this discussion.

k0k
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A submarine sonar system sends a burst of sound with a frequency of 325Hz. The sound wave bounces off an underwater rock face and returns to the submarine in 8.50s. If the wavelength of the sound is 4.71m, how far away is the rock face? (Ans: 6.51km )

--
v=fλ

λ=wavelength
f=frequency
v=velocity
--
v=fλ
v=325Hz X 4.71m
=1530.75m/s

v=d/t
d=vt
= 1530.75m/s X 8.50s
=13011.375m
=13011.375m/2
=6505.6875m

=6.51km.

What exactly am I doing wrong here? ..
 
Last edited:
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k0k said:
v=dt
d=v/t
This is not correct. What's the definition of speed? (When in doubt, check the units.)

Also: Don't forget that the sound makes a round trip.
 


Oh, my bad, a silly error. I got it now. Thanks for the tip on sound making a round trip. : )
 

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