Calculation of Maximum Velocity and Maximum Acceleration of the Ends of a Tuning Fork

Given:
Frequency of oscillation = 440 Hz
Amplitude of oscillation = 0.50 mm

(a) Maximum Velocity:
The velocity of oscillation can be calculated using the formula:
v = 2πfA
Where,
v = velocity of oscillation
f = frequency of oscillation
A = amplitude of oscillation

Substituting the given values in the formula, we get
v = 2 x π x 440 x 0.50 x 10^-3 m/s
v = 1.38 m/s

Therefore, the maximum velocity of the ends of the tuning fork is 1.38 m/s.

(b) Maximum Acceleration:
The acceleration of oscillation can be calculated using the formula:
a = (2πf)^2A
Where,
a = acceleration of oscillation
f = frequency of oscillation
A = amplitude of oscillation

Substituting the given values in the formula, we get
a = (2 x π x 440)^2 x 0.50 x 10^-3 m/s^2
a = 1.92 x 10^5 m/s^2

Therefore, the maximum acceleration of the ends of the tuning fork is 1.92 x 10^5 m/s^2.

Explanation:
When a tuning fork oscillates, its ends move back and forth. The frequency of oscillation is the number of complete oscillations that the tuning fork makes per second. The amplitude of oscillation is the maximum displacement of the tuning fork's ends from their mean position.

The maximum velocity of the tuning fork's ends occurs when the ends are at their maximum displacement from their mean position. This velocity is given by the formula v = 2πfA, where f is the frequency of oscillation and A is the amplitude of oscillation.

The maximum acceleration of the tuning fork's ends occurs when the ends are passing through their mean position. At this point, the velocity is zero, and the acceleration is maximum. The acceleration is given by the formula a = (2πf)^2A, where f is the frequency of oscillation and A is the amplitude of oscillation.

Therefore, by using the above formulas, we can calculate the maximum velocity and maximum acceleration of the ends of a tuning fork.

Max.acc,=4πAf^2