Calculating Frequency Shift in the Doppler Effect for Submarine Sonar Waves

In summary, the question asks for the frequency of the sound detected by submarine B as they approach each other head-on. Using the equation f' = f * (v+v_D)/(v-v_S), with v = 1522 m/s, v_D = 18 m/s, and v_S = 4 m/s, the calculated frequency is 1024.6 Hz. However, the website may be picky and require the exact answer of 1023 Hz.
  • #1
BoogieL80
39
0
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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  • #2
Maybe you pluged in wrong data. Your equation looks correct to me.

[tex] f' = f \frac{v+v_D}{v-v_S} [/tex]

where
[tex] v= 1522 m/s [/tex]

[tex] v_D = 18 m/s [/tex]

[tex] v_S = 4m/s [/tex]

And my answer is f'=1024.6 Hz
 
  • #3
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.
 

1. What is the Doppler Effect?

The Doppler Effect is a phenomenon where the frequency of a wave appears to change for an observer when the source of the wave is moving relative to the observer. This effect is commonly experienced with sound waves, where the pitch of a sound appears higher when the source is moving towards the observer and lower when the source is moving away.

2. How does the Doppler Effect apply to submarines?

The Doppler Effect plays a crucial role in the detection and tracking of submarines. As a submarine moves through water, it creates sound waves which can be detected by sonar equipment. The pitch of these sound waves will appear different to a stationary sonar operator compared to a moving one, due to the Doppler Effect. This allows for the determination of the submarine's speed and direction.

3. What factors affect the Doppler Effect on submarines?

The speed of the submarine, the speed of sound in water, and the relative speed between the submarine and the sonar operator are the main factors that affect the Doppler Effect on submarines. The angle at which the sound waves are emitted and received also play a role in the observed frequency shift.

4. How do scientists use the Doppler Effect to track submarines?

Scientists use sonar equipment to send out sound waves and listen for the echoes that bounce back from a submarine. The frequency of these echoes is analyzed to determine the Doppler shift, which reveals crucial information about the submarine's location, speed, and direction of travel.

5. Are there any limitations to using the Doppler Effect to track submarines?

Yes, there are limitations to using the Doppler Effect to track submarines. The speed of sound in water can vary due to changes in temperature, salinity, and pressure, which can affect the accuracy of the frequency shift measurements. Additionally, if the submarine is traveling at the same speed and direction as the sonar operator, there will be no observable Doppler shift, making it difficult to detect the submarine.

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