The tine of a tuning fork, when struck, has an amplitude of 0.25 cm. If the frequency of the fork is 150 Hz, what total distance will the tine travel in 1.00 min?
To find the total distance the tine of the tuning fork will travel in 1.00 minute, we need to first calculate the displacement produced by one full vibration or oscillation of the tuning fork.
Displacement is the maximum distance traveled from the equilibrium position. In this case, the amplitude of the tuning fork is given as 0.25 cm. Since the motion of the tuning fork is an oscillation, it will follow a harmonic motion, which is a sinusoidal wave.
The equation to describe the displacement of an object in simple harmonic motion is given by:
y(t) = A * sin(2πft)
Where:
y(t) is the displacement at time t
A is the amplitude of the oscillation
f is the frequency of the oscillation
t is the time
In this question, the amplitude A is given as 0.25 cm, and the frequency f is given as 150 Hz. Now, we can calculate the displacement produced by one full vibration by substituting the values into the equation:
Displacement = A = 0.25 cm
Now, to find the total distance traveled in 1.00 minute, we need to determine the number of vibrations or cycles the tuning fork completes in that time. One full vibration is completed when the tine returns to its starting point. This means that the tine travels a distance equal to twice the amplitude (2A) during one full vibration.
To calculate the total distance traveled in 1.00 minute, we multiply the distance traveled in one full vibration by the number of vibrations or cycles in 1.00 minute. The number of vibrations or cycles is equal to the frequency of the tuning fork (150 Hz) multiplied by the time (1.00 minute) in seconds:
Total distance = 2A * frequency * time
Converting 1.00 minute to seconds:
1.00 minute * 60 seconds/minute = 60 seconds
Plugging in the values:
Total distance = 2 * 0.25 cm * 150 Hz * 60 seconds
Now we can calculate the total distance:
Total distance = 2 * 0.25 cm * 150 Hz * 60 seconds
Total distance = 150 cm
Therefore, the tine of the tuning fork will travel a total distance of 150 cm in 1.00 minute.