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Question

The following images show a question and corresponding answer. (also see graph)
I need to understand why in the last column 1/f Hz raised to the -1 is multiplied by 10 raised to the negative 3 (especially when the length of the tube remains unchanged and plotted against the period.
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A tube with a variable length is closed at one end. A series of tuning forks is used to create resonance at the fundamental frequency for various lengths of the tube. The results obtained are shown in Table 1. 2. Table 1 Fundamental Frequeney, fTHz 200 250 300 400 500 Length, Umm 406 322 264 194 153 (a) On page 7, plot a graph of I/f against I, starting the scale on the I axis at 100 mm. [4 marks] ob) Use the graph to find the speed of sound during the experiment

Explanation / Answer

why in the last column 1/f Hz raised to the -1 is multiplied by 10 raised to the negative 3?

As you can see the values of 1/f are very small i.e., 0.005, 0.004, 0.0033, 0.0025 etc, to better interpret them we take out the common thing from them.

The common that can be taken out from all those values is 1/1000.

Since the above numbers can be written as

0.005 = 5/1000

0.004 = 4/1000

0.0033 = 3.3/1000

0.0025 = 2.5/1000

and you know, 1/1000 can be written as 1/103 which inturn can be written as 10-3.

Hence, [1/f] Hz-1 *10-3 is the convenient scale we chose for plotting a graph.

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