Question

Explain why you can't calculate the velocity of sound by taking a single measurement and dividing the time of flight into the total distance the sound pulse travels (as measured with the metre stick). (Hint: Can you assume that the line on the graph should pass through the origin? Why or why not?)

Answer 1

When you are measuring a physical quantity, you also want to know what is the error in the measurement. Beacause what you measure may not be the true value of the physical quantity. You might have made an error while performing the experiment.

When you take multiple measurements, you can quantify the error by calculating the standard deviation of all the measurements. Standard deviation gives an approximate range about the average value of the measurements in which the true value will most likely lie.

But, if you have only one measurement, you cannot calculate the standard deviation (it requires at least two measurements) so you have no way of quantifying your error. So, your measurement is useless as you cannot find a range about your measurement in which the true value could lie.

There are two types of measurement errors : systematic errors and random errors.

Systematic error is the error that you might make in every measurement (for example an offset in the meter stick). Systematic error is same for all measurements.

Random error is random in nature, it is diffferent for different measurements.

If you have made several measurements and if you are expecting a straight line profile of the measured quantity, then the random error will make the line joining the points zig zag (some points will be shifted up while some points will be shifted down from the expected line profile) and the systematic error will shift your entire line up or down (all the points shifted up or all the points shifted down from the expected line profile) and the line wil not necessarily pass through the origin.

So, if there are errors present in the measurement (which most likely are in any real world measurement), you cannot assume that the line will pass through the origin. Because the measured point may have shifted up or down from the true value depending on how much error you made in making that measurement.

Therefore you cannot calculate the velocity of sound by taking a single measurement.