Text 2. Vibrations and waves

Key terms: vibration, periodic motion, cycle, repeated pattern, transverse vibration, longitudinal vibration, amplitude, rest (equilibrium) position, period, hertz, natural frequency, phase

Vibrations and waves are among the most far-reaching and widely applied concepts in science. The vibrations of atoms and molecules control our finest clocks, make substances different colours, and even determine the transparency of materials. The transfer of vibrations in waves provides us with both sight and sound. And it is through our understanding of these concepts that we are able to probe the universe, from sub-atomic particles to distant galaxies, because our knowledge of galaxies comes to us by means of waves.

Imagine that you observe a hawk beating its wings at a constant rate, or a freely vibrating pendulum.

You will see that these vibrating types of motion will be repeated at regular intervals. All patterns of motion which repeat themselves at regular intervals, are called periodic motion. The repeated pattern is called a cycle or a vibration.

A transverse vibration occurs when the motion of the vibrating object is perpendicular to its length, as it is shown in fig. 4 (a) In a longitudinal vibration, shown in fig. 4 (b), the motion of the object is parallel to its length.

One important property of a cycle is called amplitude. Amplitude is the maximum distance of the vibrating object to its rest position or equilibrium position. In fig. 4 (a), the rest position is B, so the amplitude is the horizontal displacement between B and A, or between B and C. In fig. 4 (b), the rest position is F, so the amplitude is the vertical displacement between F and E or between F and G The time required to complete one cycle is called the period and is given the symbol T. Remember that T refers to the time for one cycle, while At represent any time interval.

N where T is the period, At is the time interval, and N is the number of cycles.

Frequency / indicates the number of cycles that occur in a unit time. Generally, we are interested in the number of cycles completed in one second. One cycle per second is called hertz (Hz). When objects are allowed to vibrate freely, they will generally do so at a specific frequency called the natural frequency.

It is often useful to compare different vibrations. Examining frequency (or period) and amplitude will provide most of the information we need. However, the vibrating objects can have identical amplitudes and frequencies, and yet be different because they are never at the same point in their cycles at the same time. The term phase is used to describe this property.

Pendulums are in the same phase if they always are either at rest or moving in the same direction at the same time. Pendulums are in the opposite phase if they are always either at rest or are moving in the opposite directions at the same time. They say the pendulums to be out of phase for any conditions between these two extremes.