SHM of a Tuning Fork: Calculating Maximum Velocity and Acceleration

In summary, the prong of a tuning fork moves back and forth 2.29 mm at a frequency of 440.2 Hz. The maximum velocity and maximum acceleration are 8.02 m/s and 22185 m/s2, respectively.
  • #1
shorti2406
12
0
Q: The prong of a tuning fork moves back and forth when it is set into vibration. The distance the prong moves between its extreme positions is 2.29 mm. If the frequency of the tuning fork is 440.2 Hz, what are the maximum velocity and the maximum acceleration of the prong? Assume SHM.


I was just hoping somebody could tell me if I did this problem correctly :smile:

For Vmax I have : (2л) x (440.2Hz) x (0.0029cm) = 8.02 m/s

For amax I have : [(2л x 440.2Hz)^2] x (0.0029cm) = 22185 m/s2


I would appreciate any input! Thanks!
 
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  • #2
shorti2406 said:
Q: The prong of a tuning fork moves back and forth when it is set into vibration. The distance the prong moves between its extreme positions is 2.29 mm. If the frequency of the tuning fork is 440.2 Hz, what are the maximum velocity and the maximum acceleration of the prong? Assume SHM.


I was just hoping somebody could tell me if I did this problem correctly :smile:

For Vmax I have : (2л) x (440.2Hz) x (0.0029cm) = 8.02 m/s

For amax I have : [(2л x 440.2Hz)^2] x (0.0029cm) = 22185 m/s2


I would appreciate any input! Thanks!

Not quite- What is the amplitude of the motion?

Plus- you will need to be a lot more careful with the units
 
Last edited:
  • #3
Oh, okay... so then:

Vmax : (2л) x (440.2Hz) x (0.00229m) = 6.33 m/s

amax : [(2л x 440.2Hz)^2] x (0.00229m) = 17518 m/s2

Does that look about right? Or am I still way off?
 
  • #4
The amplitude is still not correct.
 
  • #5
Well, I think I'm just stuck then. Can anybody give me a clue as to what the correct amplitude shoudl be? I would really appreciate it!
 
  • #6
shorti2406 said:
Well, I think I'm just stuck then. Can anybody give me a clue as to what the correct amplitude shoudl be? I would really appreciate it!
You'll smack yourself in the head when you realize it:
The distance the prong moves between its extreme positions is 2.29 mm.

Remember that amplitude is the maximum displacement from the equilibrium position, not the distance between the extreme positions.
 
  • #7
You're right. I have no idea why I didn't realize that! Thank you so much for you help.
 

Related to SHM of a Tuning Fork: Calculating Maximum Velocity and Acceleration

1. What is SHM (Simple Harmonic Motion)?

SHM is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium and always directed towards the equilibrium point.

2. How does a tuning fork exhibit SHM?

A tuning fork exhibits SHM because when it is struck, it vibrates back and forth with a constant frequency due to the elastic restoring force of the metal tines.

3. What factors affect the frequency of SHM in a tuning fork?

The frequency of SHM in a tuning fork is affected by the length, mass, and stiffness of the tines, as well as external factors like temperature and air resistance.

4. Can the amplitude of SHM in a tuning fork be changed?

Yes, the amplitude of SHM in a tuning fork can be changed by altering the force applied to the tines. However, this will not change the frequency of the motion.

5. How is SHM in a tuning fork used in scientific experiments?

SHM in a tuning fork is used in experiments to measure frequencies and to calibrate instruments such as oscilloscopes and accelerometers. It is also used in musical instruments and clocks.

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