How Long Does It Take to Hear a Stone Hit the Bottom of a Shaft?

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Homework Help Overview

The problem involves determining the total time it takes for a stone dropped into a 122.5 m deep mine shaft to be heard after it hits the bottom. The subject area pertains to kinematics and sound propagation.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss calculating the time for the stone to fall and the time for the sound to travel back up the shaft. There is confusion regarding the relationship between sound velocity, wavelength, and frequency, particularly in the context of this problem.

Discussion Status

Some participants have made attempts to calculate the time for the stone's fall and the sound's return, while others are questioning the necessity of frequency in their calculations. There appears to be a productive exchange of ideas, but no consensus has been reached on the correct approach.

Contextual Notes

Participants note a lack of reference in textbooks regarding the specific relationship between sound properties and the problem setup, contributing to confusion about the required calculations.

ahrog
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Homework Statement


Someone drops a stone into a mine shaft 122.5 m deep. How soon after she drops the stone does she hear it hit the bottom of the shaft?


Homework Equations


v= wavelength x frequency


The Attempt at a Solution


I changed the equation to be:
d/t=wf
t=d/wf
t=122.5m/(343m/s x f)

And I'm stuck there...I don't get how to get the frequency

My textbook doesn't even refer to something like this, so I'm extremely confused...It's like asking someone about something they've never learned before...
 
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First you need to figure the time for it to fall 122.5m, then add the time for the sound to return.

Δt = D/Vsound
 
I got the falling part time to be 5 seconds.

And for the time for the sound to return, how do I figure that out? If the velocity for the sound is wavelength x frequency which I have only the wavelength, how can I find the time?
 
t=122.5m/(343m/s x f)
Here f in not needed. time = distance/velocity.
 

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