Doppler Effect II (Both observer and source in motion)

In summary, the conversation discusses calculating the frequency a person hears when an eagle flies directly towards them at a certain speed and emits a sound at a certain frequency. The equation used for this calculation is provided and the mistake made in the initial attempt is identified and corrected. The final calculated frequency is confirmed to be correct.
  • #1
exi
85
0

Homework Statement



You're flying in an aircraft at 46 m/s. An eagle flies directly towards you at 11 m/s. Speeds are relative to ground.

The eagle emits a cry at 3400 Hz, and the speed of sound is 330 m/s. What frequency do you hear?

Homework Equations



[tex]f_o = f_s\left( \frac{1\pm\frac{v_o}{v}}{1\mp\frac{v_s}{v}} \right)[/tex]

Because the observer and source are both moving towards each other (presumably?),

[tex]f_o = f_s\left( \frac{1+\frac{v_o}{v}}{1-\frac{v_s}{v}} \right)[/tex]

The Attempt at a Solution



Seems simple enough, but

[tex]f_o = 3400\left( \frac{1+\frac{46}{330}}{1-\frac{11}{330}} \right)[/tex]

Works out to 4902.8213 Hz, a wrong answer. This problem seemed straightforward, but I'm not sure what I'm missing.
 
Last edited:
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  • #2
Check your math. That's not what I get.
 
  • #3
Dick said:
Check your math. That's not what I get.

Don't I feel silly, part 2.

4007.5235 Hz. I've got only one remaining shot at that problem; I didn't make any other conceptual mistakes, correct?
 
  • #4
That's what I get, but I'm not claiming infallibility.
 
  • #5
Dick said:
That's what I get, but I'm not claiming infallibility.

It's correct.

Thanks much, sir; I'll just whistle and blame my calculator now.
 

1. What is the Doppler Effect II?

The Doppler Effect II is a phenomenon in physics that describes the perceived change in frequency of a wave when both the observer and the source of the wave are in motion relative to each other.

2. How does the motion of the observer and source affect the perceived frequency of a wave?

When both the observer and the source are moving towards each other, the perceived frequency of the wave increases. Conversely, when they are moving away from each other, the perceived frequency decreases. The amount of change in frequency is directly proportional to the speed of the objects' motion.

3. What is the difference between the Doppler Effect I and II?

The Doppler Effect I only considers the motion of either the observer or the source, while the Doppler Effect II takes into account the motion of both the observer and the source. This means that the perceived frequency of a wave can change even when both the observer and source are in motion in the same direction.

4. Can the Doppler Effect II be observed in everyday life?

Yes, the Doppler Effect II can be observed in various everyday situations, such as the change in pitch of a siren of an ambulance as it approaches and passes by, or the change in pitch of a car horn as it passes by while the observer is also in motion.

5. What is the significance of the Doppler Effect II in science and technology?

The Doppler Effect II has various applications in science and technology, including radar and sonar systems, medical imaging, and astronomical observations. It helps scientists and engineers understand and measure the motion and velocity of objects in space and on Earth.

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