Find the frequency of a tuning fork
that takes 3.04 times 10 to the negative third seconds to complete one
A tuning fork is a device usually
made of metal that’s designed to oscillate at a very particular frequency when it’s
As the name implies, a tuning fork
is used as a standard to use in order to tune things that need to be matched to a
certain frequency, such as for example, musical instruments.
Now, if we were to strike a tuning
fork, say against the palm of our hand, then the fork will begin to oscillate at a
very particular frequency, its resonant frequency, the frequency it’s made to move
at by design.
We’re told that as this tuning fork
vibrates, each one of its oscillations takes 3.04 times 10 to the negative third
seconds to complete.
That, the time taken to complete
one oscillation, is known as the period of oscillation. And it’s often abbreviated with a
capital 𝑇. Based on this period, we want to
solve for the frequency of the tuning fork.
There’s a helpful relationship
between these two variables, frequency and period. And that is that they’re inverses,
one of another. Frequency is equal to one over
period. And if we were to flip it around,
period is equal to one over frequency.
But since we want to solve for
frequency, we’ll keep it in the form given. 𝑓 is equal to one over 𝑇, which
is equal to one over 3.04 times 10 to the negative third seconds. This is equal to 329 inverse
seconds or 329 Hz.
This is a frequency audible to the
human ear. And it’s the frequency of this
tuning fork’s oscillations.