Nature of Waves
Vibrations or oscillations are closely related to waves. Waves are created whenever objects vibrate or oscillation.
* A repeated motion that occurs back and forth over the same path at regular intervals. Examples:
* A Child on a swing
* A wrecking ball swaying to and fro
* A swinging pendulum of a grandfather clock
Simple Harmonic Motion (SHM)
* Is a type of motion along a straight path in which the acceleration is proportional to the displacement of the object from its equilibrium position and is always directed toward the equilibrium position. * Simple harmonic motion maybe described by its amplitude, period, and frequency. Amplitude (A)
* The maximum displacement.
* The time needed to repeat one complete cycle or vibration. Frequency (f)
* Is the number of cycles per second.
Period and frequency are reciprocals of each other. In equation form: T=1f and f=1T
The unit used in expressing period is second, while the unit for frequency is 1/second or cycle per second (c/s). It is also called Hertz (Hz), after Heinrich Hertz, one of the pioneers in the study of electromagnetic waves. The following statements are true for a simple ideal type of pendulum. 1. Provided that a pendulum vibrates in a vacuum, the period T is independent of the mass. 2. The period T is independent of the amplitude if the angle is relatively small, say 10° or less. For such small angles of displacement, the pendulum’s motion is simple harmonic. 3. The period is directly proportional to the square root of its length. With two pendulums of different lengths, the longer one will have a period longer than that of the shorter one. T1T2 = l1l2
4. The period T is inversely proportional to the square root of the acceleration due to gravity. T = 2π 1g
T = period of time
L = length of the string
G = acceleration due to gravity, 9.8 m/s2 near earth’s surface Sample Problem:
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