Calculating Percentage Error in Canyon Depth Ignoring Sound Time

In summary, the conversation discusses the calculation of the depth of a canyon by taking into account the time it takes for a stone to fall and the sound of it hitting the bottom. The correct calculation is found to be 648.9 m, while the incorrect calculation that ignores the sound travel time is 879.844 m. This results in a percentage error of 26.2%. The conversation also discusses setting up equations and solving for the times to incorporate the sound travel time into the calculation.
  • #1
munther
11
0
A stone is dropped into a deep canyon and is heard to strike the bottom 13.4 s after release (the speed sound is 343m/s) What would be the percentage error in the depth if the time required for the sound to reach the canyon rim were ignored?

I found the depth of the canyon =2298m
then what is the next step?
 
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  • #2
How did you do calculate the depth?

The point is to calculate it two ways: once ignoring the time for the sound to travel; once taking it into account.
 
  • #3
sorrry
the distance = 1/2 a t^2
= .5 x 9.8 x (13.4/2)^2 = 219.961 m^2


that is when i take the time into account

but how i will not take it??
 
Last edited:
  • #4
munther said:
the distance = 1/2 a t^2
= .5 x 9.8 x (13.4/2)^2 = 219.961 m^2
The time needed here is the time that the stone was falling. Why did you divide by 2?

Think of the time to hear the echo as having two parts:
(1) The time that the stone was falling.
(2) The time it takes for the sound of the stone hitting the canyon floor to travel up to the top.

Time #1 + Time #2 = 13.4 seconds

Since sound travels pretty fast compared to the stone, time #2 will be small.
 
  • #5
ok that is very good

then how i will divide the time between the falling and the echo
 
  • #6
munther said:
then how i will divide the time between the falling and the echo
To incorporate the time delay due to the speed of sound, you'll need to set up equations and solve for the times. Hint: Set up two equations (one for the falling rock; one for the sound) relating distance and time.
 
  • #7
ok

d= .5xgxt1 = 343t2
t1+t2 =13.4
by solving both equations
t1= 11.51
t2= 1.89

then the depth = 648.9 m

is it right


next step:

%=(depth1-depth2)x100/(depth1)

we found one depth

the second depth when we ignored the time
is the second depth when time = 13.4 for the d=.5x9.8xt
 
  • #8
munther said:
ok

d= .5xgxt1 = 343t2
t1+t2 =13.4
by solving both equations
t1= 11.51
t2= 1.89

then the depth = 648.9 m

is it right
Looks good to me.
is the second depth when time = 13.4 for the d=.5x9.8xt
Right. (You have a typo in your formula--that should be t^2.)
 
  • #9
thanks

i posted it ...but it is wrong!

(879.844-648.9)/(879.844)=26.2% xxx Wrong xxx !

why??
 
  • #10
munther said:
thanks

i posted it ...but it is wrong!

(879.844-648.9)/(879.844)=26.2% xxx Wrong xxx !

why??
You need to read the question very carefully. I think they are asking for the percentage error the incorrect method (that ignores the sound travel time) introduces with respect to the correct method. The correct measurement should be in the denominator.
 

1. What is percentage error in calculating canyon depth ignoring sound time?

Percentage error in calculating canyon depth ignoring sound time is a measure of how much the calculated value differs from the actual value. It is expressed as a percentage and can be used to evaluate the accuracy of a measurement or calculation.

2. How is percentage error calculated?

Percentage error is calculated by taking the absolute value of the difference between the calculated value and the actual value, dividing that by the actual value, and then multiplying by 100. The resulting value is the percentage error.

3. Why is sound time ignored in calculating canyon depth?

Sound time is often ignored in calculating canyon depth because it is a relatively small factor compared to other measurements, such as the depth of the canyon. Additionally, sound time can be affected by external factors, such as water temperature and salinity, which can introduce errors into the calculation.

4. What are some potential sources of error in calculating canyon depth ignoring sound time?

There are several potential sources of error in calculating canyon depth ignoring sound time. These can include measurement errors, environmental factors such as water temperature and salinity, and uncertainties in the equipment used to make the measurements.

5. How can percentage error in canyon depth calculations be minimized?

Percentage error in canyon depth calculations can be minimized by using accurate and precise measurement techniques, calibrating equipment regularly, and accounting for any known sources of error. Additionally, taking multiple measurements and calculating an average can also help to reduce the overall percentage error.

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