Doppler question - find the observed frequency

[JoeyBob]

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?

 

[Steve4Physics]

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.

 

[JoeyBob]

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?

 

[Steve4Physics]

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..