The displacement of an object is given by y = (4.6 cm) sin 28ðt. (a) What is the amplitude? (b) What is the frequency? (c) What is the period?
To determine the answers to these questions, we need to understand the equation given: y = (4.6 cm) sin(28πt).
(a) Amplitude: The amplitude of a wave represents the maximum displacement of the object from its equilibrium position. In the given equation, the amplitude is given as 4.6 cm. Therefore, the answer to part (a) is 4.6 cm.
(b) Frequency: The frequency of a wave represents the number of complete oscillations or cycles the object makes in one second. In the given equation, the coefficient of "t" is 28π, which defines the angular frequency (ω), not the frequency (f). However, we can use the relation between angular frequency and frequency:
ω = 2πf
Solving for f, we have:
f = ω / (2π) = (28π) / (2π) = 14 Hz
Therefore, the frequency is 14 Hz.
(c) Period: The period of a wave represents the time it takes for the object to complete one full cycle of oscillation. The period (T) is the reciprocal of the frequency:
T = 1 / f = 1 / 14 Hz
Simplifying:
T ≈ 0.0714 s
Therefore, the period is approximately 0.0714 seconds.