The A above middle C has a frequency of 440 Hz. If you play this note on a piano and the piano string oscillates with an amplitude of 0.55 mm, what is the maximum acceleration of the string?
To find the maximum acceleration of the vibrating piano string, we need to use the equation relating frequency, amplitude, and acceleration for an object in simple harmonic motion. The equation is as follows:
a = 4π²f²A
Where:
a = maximum acceleration
f = frequency of the vibration
A = amplitude of the vibration
In this case, the frequency is given as 440 Hz, and the amplitude is given as 0.55 mm (which we'll convert to meters). We can now substitute these values into the equation and solve for the maximum acceleration.
First, let's convert the amplitude from millimeters to meters:
0.55 mm = 0.55 × 10^(-3) m
Now, we can substitute the values into the equation:
a = 4π²(440 Hz)²(0.55 × 10^(-3) m)
Calculating this expression will give us the maximum acceleration of the string.