A piano tuner strikes a tuning fork for note A above middle C and sets in motion vibrations that can be modeled by the equation y = 0.001 sin 880 Pi(T). Find the amplitude and period for the function.
amplitude : .001
period = 2π/(880π) = 1/440
iog
65
To find the amplitude and period of the given function y = 0.001 sin 880π(T), we can analyze the equation.
1. Amplitude: The amplitude of a sinusoidal function represents the maximum displacement from the mean value. In the given equation, the coefficient before the sine function, 0.001, represents the amplitude. Therefore, the amplitude is 0.001.
2. Period: The period of a sinusoidal function refers to the length of one complete cycle. In the given equation, the period is influenced by the coefficient before T in the argument of the sine function. In this case, the coefficient is 880π. To find the period, we can use the formula T = 2π/ω, where ω is the angular frequency. In our equation, ω = 880π, so the period is T = 2π/(880π) = 1/440 seconds.
Hence, the amplitude is 0.001 and the period is 1/440 seconds.