# Simple Harmonic Motion Tuning Fork Question

• ninjagowoowoo
In summary, the conversation is about calculating the maximum speed of the tip of a prong on a tuning fork that vibrates at a frequency of 264 Hz and has an amplitude of 1.66 mm. The equation Vmax = omega*A is being used, but there is uncertainty about finding the value of A. The mistake is realized and the correct equation is determined to be Vmax = (2pi/T)(A) where T is the period of the vibration. The conversation ends with the issue being resolved and thanks being given.
ninjagowoowoo
Q:
A tuning fork vibrates at a frequency of 264 Hz and the tip of each prong moves 1.66 mm to either side of center. Calculate the maximum speed of the tip of a prong.

So far I've found that Vmax = omega*A, but I don't know how to find A. Am I going in the wrong direction? Or is there a way to find A that I don't know about yet..?

ninjagowoowoo said:
... the tip of each prong moves 1.66 mm to either side of center.
That's the amplitude.

Oh haha, I knew it must've been something stupid, thanks.

Ok so I figured that Vmax would be omega*A, but it isn't correct. I know that
v=-omega*A*sin(omega*t) (yeah I need to learn how to write equations better)

so I assumed that in the problem, it's basically an initial value, so t=0. So that would leave v=omega*A.

From this I got Vmax = (2pi/T)(A)
and T=1/f

so Vmax = (2pi/(1/f))(A)

I guess this is incorrect. Oh and I didnt forget to convert mm to m. Any pointers?
Thanks

woops nevermind... I must have entered it in my calculator wrong haha sorry. Thanks for the help Al.

## What is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is proportional to the displacement from equilibrium and is directed towards the equilibrium position. It is a key concept in physics and is commonly observed in objects that oscillate, such as springs and pendulums.

## What is a tuning fork?

A tuning fork is a small metal object with two prongs that vibrate at a specific frequency when struck. It is commonly used to produce a pure tone for tuning musical instruments or for scientific demonstrations.

## How is a tuning fork related to Simple Harmonic Motion?

The prongs of a tuning fork vibrate back and forth in SHM when struck, producing a pure tone at a specific frequency. The frequency of the tone is determined by the mass, length, and stiffness of the prongs.

## How can I calculate the frequency of a tuning fork?

The frequency of a tuning fork can be calculated using the equation f = 1/T, where f is the frequency and T is the period of the vibration. The period can be measured by timing the number of vibrations in a certain amount of time.

## How is the frequency of a tuning fork affected by changes in mass, length, and stiffness?

The frequency of a tuning fork is directly proportional to the square root of the stiffness and inversely proportional to the square root of the mass and length. This means that an increase in stiffness or a decrease in mass or length will result in a higher frequency, and vice versa.

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