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 2.28 mm. If the frequency of the tuning fork is 440.6 Hz, what are the maximum velocity and the maximum acceleration of the prong? Assume SHM.

Question

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 2.28 mm. If the frequency of the tuning fork is 440.6 Hz, what are the maximum velocity and the maximum acceleration of the prong? Assume SHM.

I know that similar questions have been posted before, but some weren't answered and some where confusing, so if someone could help please!

Answer 1

So what is Vm m/s

and Am m/s^2

Thank you!

Answer 2

x = 1.14 * 10^-3 sin 2 pi f t

in meters
f = 440.6
so w = 2 pi f = 2768 radians/s

x = 1.14 * 10^-3 sin 2768 t
v = 1.14*10^-3*2768 cos 2768 t
a = -1.14*10^-3*2768^2 sin 2768 t

v max = 1.14*10^-3*2768 = 3.16 m/s
a max = 2768 v max = 8736 m/s^2

Answer 3

To find the maximum velocity and maximum acceleration of the prong, we can use basic principles of simple harmonic motion (SHM). In SHM, the displacement, velocity, and acceleration of an oscillating object are related to its frequency and amplitude.

1. Maximum velocity (v_max):
The maximum velocity of an object undergoing SHM is given by the product of the amplitude (A) and the angular frequency (ω).

v_max = A * ω

The angular frequency, ω, can be calculated using the formula:

ω = 2πf

Where f is the frequency of the tuning fork.

Given:
Amplitude (A) = 2.28 mm = 0.00228 m (since 1 mm = 0.001 m)
Frequency (f) = 440.6 Hz

First, we need to convert the frequency from Hz to angular frequency (rad/s) by multiplying it by 2π:

ω = 2π * 440.6

Now, we can calculate the maximum velocity:

v_max = A * ω
= 0.00228 * (2π * 440.6)

Simplifying this expression will give us the maximum velocity of the prong.

2. Maximum acceleration (a_max):
The maximum acceleration of an object undergoing SHM is given by the product of the amplitude (A) and the angular frequency squared (ω^2).

a_max = A * ω^2

Using the angular frequency obtained in the previous step, we can calculate the maximum acceleration:

a_max = A * ω^2
= 0.00228 * (2π * 440.6)^2

Simplifying this expression will give us the maximum acceleration of the prong.

By plugging in the values and performing the calculations, you will be able to find the maximum velocity and maximum acceleration of the prong of the tuning fork.