Resonance With Tuning Fork

Classical Mechanics Level 1

Resonance is a special case of forced vibrations. When the frequency of an externally applied periodic force on a body is equal to its natural frequency, the body readily begins to vibrate with an increased amplitude. This phenomenon is known as resonance. The vibrations of large amplitude are called resonant vibrations.

With which of the following frequencies does a tuning fork of $256\text{ Hz}$ resonate?

Try my World of Physics to solve many problems like this one.

288 314 332 512

3 solutions

Ram Mohith
Jun 4, 2018

Relevant wiki: Sound

A tuning fork of $256 Hz$ means that the fundamental frequency of vibration of fork is 256 Hz.

Now, resonance occurs when the fork vibrates with a frequency equal to fundamental frequency or a frequency that is a multiple of fundamental frequency.

From the given options $512 Hz$ is a multiple of $256 Hz$ .

Therefore, $\color{#20A900}\text{The tuning fork resonate with 512 Hz.}$

@Ram Mohith Typo in last line bro.........it should be 512Hz..........!!!

Aaghaz Mahajan - 3 years ago

Thanks for informing me . I have updated my solution.

Ram Mohith - 3 years ago

That's interesting. With electrical circuits (LC circuits, for example), the resonances don't have this integer multiple property.

Steven Chase - 3 years ago

Will 128 Hz also make it resonate

Shubham Maurya - 2 years, 7 months ago

I think only integer multiples of 256 will resonate.

Ram Mohith - 2 years, 7 months ago

I also am sure that in electrical engineering the thing about resonance is not the same as this.

Meep Labs - 2 years, 3 months ago

J B
Aug 6, 2018

The primary mode of vibration is shown, and the first harmonic is the answer, but tuning forks and most mechanically resonant systems have secondary modes of resonance at other frequencies that include harmonics of those frequencies, and all interaction among the various frequencies (mixing-> sum and difference). For example, the tuning fork arms can also vibrate perpendicular to the screen, the handle can 'wiggle' in other directions, and at significantly higher frequencies, those components can resonate lengthwise.

Max Yuen
May 3, 2019

I don’t think 512Hz is right, since you will need to justify this with a modal profile that make sense. If one does a physical simulation on the eigenmodes of the two pronged tuning fork, you will not get the 512Hz as the next resonant frequency.

It is as bizarre a generalization as saying a half closed pipe with fundamental resonance at 256Hz would also be resonant at 512Hz.

Resonance With Tuning Fork

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