A point on the end of a tuning fork moves in simple harmonic motion described by d = a sin ωt. Find ω given that the tuning fork
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Answer:
The percentage uncertainty in the average speed is 0.10% (2 sig. fig.)
Explanation:
Consider the formula for average speed .
,
where
is the total distance, and
is the time taken.
The percentage uncertainty of a fraction is the sum of percentage uncertainties in
- the numerator, and
- the denominator.
What are the percentage uncertainties in and
in this question?
The unit of the absolute uncertainty in is meters. Thus, convert the unit of
to meters:
.
.
The unit of the absolute uncertainty in is seconds. Convert the unit of
to seconds:
Similarly,
.
The average speed here is a fraction of
and
. Both
and
come with uncertainty. The percentage uncertainty in
will be the sum of percentage uncertainties in
and
. That is:
.
Generally, keep
- two significant figures for percentage uncertainties that are less than 2%, and
- one for those that are greater than 2%.
The percentage uncertainty in here is less than 2%. Thus, keep two significant figures. However, keep more significant figures than that in calculations to make sure that the final result is accurate.