Doppler question - find the observed frequency

AI Thread Summary
The discussion focuses on calculating the observed frequency using the Doppler effect, where the initial calculations yield an incorrect frequency of 86.1477 instead of the expected 88.47. The error stems from misunderstanding the total time of 9.0 seconds, which includes both the fall time and the sound travel time, indicating that the fall time is less than 9.0 seconds. Additional mistakes noted include not specifying units for acceleration and frequencies, as well as incorrect significant figures. To find the final velocity without a given drop distance, participants suggest constructing two equations based on the distances covered by the falling object and the sound, leading to a quadratic equation for time. This approach provides a clearer path to resolving the frequency calculation issue.
JoeyBob
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Homework Statement
see attached
Relevant Equations
fobs= ((v-vo)/(v-vs))fs
So first I calculate the final velocity by multiplying the time by the acceleration, 9.8, to get 88.2 m/s.

Now I use the equation. (343/(343-(-88.2))*108.3 = 86.1477.

But the answer should be 88.47. What am I doing wrong here?
 

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9.0s is not the time it takes to fall. It is the time it takes to fall plus the time the sound takes to travel to the surface. So the time it takes to fall is less than 9.0s.

Other mistakes are:
- stating the acceleration is 9.8 without giving the unit;
- giving values for the final frequency and the 'official answer' frequency without giving the unit;
- rounding your answer to an incorrect number of significant figures.
 
Steve4Physics said:
9.0s is not the time it takes to fall. It is the time it takes to fall plus the time the sound takes to travel to the surface. So the time it takes to fall is less than 9.0s.

Other mistakes are:
- stating the acceleration is 9.8 without giving the unit;
- giving values for the final frequency and the 'official answer' frequency without giving the unit;
- rounding your answer to an incorrect number of significant figures.
How would one calculate the final velocity then if distance of the drop isn't given?
 
JoeyBob said:
How would one calculate the final velocity then if distance of the drop isn't given?
If the time it takes to fall is T, then the time for the sound to travel back up is (9.0-T).

You can construct 2 equations:
- one equation for the distance covered by the noisemaker in time T;
- one equation for the distance covered by the sound in time (9.0 - T).
Since these 2 distances are the same you get a quadratic equation for T which you solve..
 
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