Video: Calculating Percent Relative Error

In an experiment, the speed of sound waves on Earth at sea level at a temperature of 21°C is 333 m/s. Find the percent relative error in the measurement using an accepted value of 344 m/s. Give your answer to one decimal place.

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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.

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