Question

A stroboscope was used to determine the frequency of the string oscillator. Strobe frequencies f_s were recorded where a single stationary image of the oscillating string was observed. The frequency of the oscillator f can be determined from the stroboscope frequencies f_s by f = nf_s where n is an integer corresponding to the number of oscillations per flash. The strobe frequencies produced were determined and tabled below:

Strobe Frequency fs Hz	Oscillations per flash n
22.2	m
14.4	m+1
11.1	m+2
9.2	m+3

m an integer, is determined to be 2.

The oscillator frequency is determined to be f = 44.50 Hz, from the average of nf_s.

Use the mean error technique to determine the uncertainty f. Express the answer to two decimal places, with the SI unit included.

Answer:

Answer 1

We observe that fs is halved when m becomes m+2 (fs changes from 22.6 to 11.1).

This can only occur if the number of oscillations per flash has halved.

That means that:

m/(m+2) = 1/2.

m+2 = 2m

m =2

For m, n = 2: f = 2x22.2 = 44.4Hz

For m+1, n = 2+1 = 3: f = 3x14.4 = 43.2Hz

For m+2, n = 2+2 = 4: f = 4x11.1 = 44.4Hz

For m+3, n = 2+3 = 5: f = 5x9.2 = 46.0Hz

Find the average of these 4 frequencies:

= (44.4 + 43.2 + 44.4 + 46.0)/4

= 44.50 Hz

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