Question Video: Calculating the Frequency of an Oscillation from Its Period

Find the frequency of a tuning fork that takes 3.04 × 10⁻³ s to complete one oscillation.

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Video Transcript

Find the frequency of a tuning fork that takes 3.04 times 10 to the negative third seconds to complete one oscillation.

A tuning fork is a device usually made of metal that’s designed to oscillate at a very particular frequency when it’s struck.

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.

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