The discussion centers on calculating the percentage error in canyon depth when ignoring the time it takes for sound to travel. The correct depth of the canyon, accounting for sound travel time, is determined to be 648.9 meters, while the incorrect calculation yields 879.844 meters. The percentage error is calculated using the formula % = (depth1 - depth2) x 100 / depth1, where depth1 is the correct measurement. The final percentage error, when calculated correctly, is 26.2%.
PREREQUISITESStudents and educators in physics, engineers involved in acoustics, and anyone interested in understanding the implications of ignoring sound travel time in measurements.
The time needed here is the time that the stone was falling. Why did you divide by 2?munther said:the distance = 1/2 a t^2
= .5 x 9.8 x (13.4/2)^2 = 219.961 m^2
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.munther said:then how i will divide the time between the falling and the echo
Looks good to me.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
Right. (You have a typo in your formula--that should be t^2.)is the second depth when time = 13.4 for the d=.5x9.8xt
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.munther said:thanks
i posted it ...but it is wrong!
(879.844-648.9)/(879.844)=26.2% xxx Wrong xxx !
why??