Video Transcript
In an experiment, the speed of
sound waves on Earth at sea level at a temperature of 21 degrees Celsius is 333
meters per second. Find the percent relative error in
the measurement using an accepted value of 344 meters per second. Give your answer to one decimal
place.
So, in this scenario, we’re talking
about making a measurement of the speed of sound waves where, under certain
conditions, at sea level and at a particular temperature, we measure a sound wave
speed of 333 meters per second. We can call that measured speed 𝑠
sub m. And we’re to compare it to an
accepted speed of sound, we’ll call that 𝑠 sub a, of 344 meters per second at the
same elevation and temperature. Knowing these values, we want to
calculate the percent relative error in our measurement. To help us figure this out, we can
recall the equation for the percent relative error of a measured value. It’s equal to the magnitude of the
accepted value minus the measured value all divided by the accepted value and then
multiplied by 100 percent.
We can apply this relationship to
our scenario by substituting 𝑠 sub a for the accepted value and 𝑠 sub m for the
measured value. And that gives us this
expression. And when we subtract 333 meters per
second from 344, we get a value in our numerator of 11 meters per second. Notice now that these units, meters
per second, cancel out. And when we calculate 11 divided by
344 multiplied by 100 percent to one decimal place, we get a result of 3.2
percent. This is the percent relative error
in our measurement.
