Calculating Frequency Shift in the Doppler Effect for Submarine Sonar Waves

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SUMMARY

The discussion focuses on calculating the frequency shift of sonar waves in the Doppler Effect as experienced by two submarines approaching each other. Submarine A, traveling at 4 m/s, emits a sonar wave at 1010 Hz, while Submarine B moves towards it at 18 m/s. The correct formula used is f' = f * (v + v_D) / (v - v_S), where v is the speed of sound in salt water (1522 m/s), v_D is the speed of Submarine B (18 m/s), and v_S is the speed of Submarine A (4 m/s). The accurate frequency detected by Submarine B is approximately 1024.6 Hz, highlighting the importance of precise calculations in Doppler Effect scenarios.

PREREQUISITES
  • Understanding of the Doppler Effect
  • Familiarity with sonar wave principles
  • Basic knowledge of speed and velocity concepts
  • Proficiency in algebraic manipulation of equations
NEXT STEPS
  • Study the Doppler Effect in various mediums, including air and water
  • Learn about sonar technology and its applications in underwater navigation
  • Explore advanced topics in wave mechanics and frequency analysis
  • Investigate the impact of relative motion on wave propagation
USEFUL FOR

This discussion is beneficial for physicists, engineers, and students studying acoustics, particularly those interested in underwater sonar technology and the Doppler Effect.

BoogieL80
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I'm working on the following problem:

Two submarines are underwater and approaching each other head-on. Sub A has a speed of 4 m/s and sub B has a speed of 18 m/s. Sub A sends out a 1010 Hz sonar wave that travels at a speed of 1522 m/s.

The question asks two questions, but I'm stuck on the first one:

What is the frequency of the sound detected by sub B (to the nearest Hz)?

I was using the formula frequencyobserver = frequencysource * 1 + (vobserver / velocity of sound) / 1 - (vsource / velocity of sound). I assumed that the numerator would use the positive sign since the observer is moving towards the source. I used the minus sign in the denominator since the source is moving towards the observer. For the speed of sound I used 1522 m/s since the submarines are traveling in salt water. I then multiply my calculated numbers times 1010 and got a frequncy of 1019 Hz. However webassign is telling me this is incorrect. Any help with what I'm doing wrong?
 
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Maybe you pluged in wrong data. Your equation looks correct to me.

f' = f \frac{v+v_D}{v-v_S}

where
v= 1522 m/s

v_D = 18 m/s

v_S = 4m/s

And my answer is f'=1024.6 Hz
 
My goodness, that thing was too picky. I put in 1023 Hz the first time and it didn't accept the number. Thank you for your help.
 

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