Waves Basics

Expectations Upon completion of this unit you will be able to: Define waves and wave pulses. Identify the two types of wave pulses. Define transverse wave pulses. Define longitudinal wave pulses. Compare and contrast the two types of waves. Identify the parts of a wave. Calculate wave energy using the amplitude formula. Define wavelength, frequency, period and wave velocity. Using the appropriate formulas, solve for wavelength, frequency, period and wave velocity. Demonstrate an understanding of the wave equation.

When you first think of waves, but as you will see in this unit, waves come in many forms. The vibration that creates a wave can either be a single vibration (wave pulse) or one which repeats itself over time. The vibrations which repeat themselves give rise to what are known as continuous, or periodic, waves. Most of the waves you will study are periodic waves.

Types of Waves Waves can be divided into two broad categories: Mechanical waves: These waves require a medium (some substance) in order to propagate or move. Water and sound waves are examples of this type of wave. Electromagnetic waves: These waves do not require a medium in order to propagate. However, they can move through a medium if one is present. Examples of this type of wave include visible light and microwaves. In physics, electromagnetic is often abbreviated as EM.

Mechanical Waves There are two different types of mechanical waves. Transverse waves: The wave motion is in a direction that is perpendicular to the motion of the medium itself. You will see examples of these types of waves on a piano wire when the keys are struck and if you shake a slinky back and forth. Longitudinal waves: The wave motion is in a parallel direction to the motion of the medium itself. Examples of this type of wave include sound waves and the waves formed by compressing the coils of a slinky

Many people, after observing a mechanical wave, assume that the wave is itself matter. This is not true. Waves are vibrations that move without actually carrying the matter with them. A water wave may cover great distances, but the actual water particles only move a small amount and tend to return to their original position after the wave has passed.

Wave Anatomy There are characteristics that all waves share and you will need to be able to discuss them. To make things easier, transverse waves will be used to illustrate the explanations and examples. Keep in mind that all of the characteristics still apply to longitudinal waves. At the end of this section, you will see how to illustrate a longitudinal wave as a transverse wave.

The high points of the wave are called crests and the low points, troughs. The "middle" position is called the equilibrium (or rest) position/level. The maximum displacement of the wave from its equilibrium is given the symbol A and is called the amplitude.

Waves transport energy The amplitude of a wave is a measure of how much energy the wave is transporting (water waves). To be precise, the energy transported by a wave is proportional to the square of the amplitude. (E  A 2 ) What this means is, for example, if you double the amplitude of a wave, you actually increase the energy it transports by a factor of 2 2, or 4.

Wavelength The wavelength of a wave is often defined as the distance between two successive crests.

To be more precise, it is the distance between any two successive points where the wave motion repeats Symbol - (called lambda) Units - m

Frequency A typical radio can receive radio waves at several different frequencies. AM signals are in the kHz range while FM signals are in the MHz range.

Frequency The frequency is the number of complete wave cycles that pass a given point per unit time. Frequency is given the symbol f and is measured in units of waves/second. In SI the #/s is known as hertz (Hz). When you tune in a radio station at 97.5 MHz, it means that your radio receives 9.75 × 107 waves every second. Closely related to frequency is the measurement called period.. The period of a wave is the time needed for the wave motion to repeat. The period is just the reciprocal of frequency which leads to your first formula:

Wave Velocity The wave velocity (speed) is the velocity at which any part of the wave moves. It is not the velocity of the particles in the medium. The simplest way of calculating the wave velocity is to take the distance travelled and divide it by the time taken. For a wave, the distance travelled could be a wavelength and it would cover this distance in a time equal to the period. In this case, the velocity (v) is equal to frequency over period, shown below: V = /T

Usually, the period T is replaced by 1/f, so the formula for velocity becomes: v = f λ This equation is sometimes known as the wave equation and it applies to all the wave types you have seen so far in this unit. Unless otherwise stated, you can assume that electromagnetic waves travel at a speed of 3.00 × 108 m/s.

Examples A radio station is broadcasting at 97.5 MHz. If the radio waves (like most electromagnetic waves) travel at a velocity of 3.00 × 108 m/s, determine the wavelength of the radiowaves.

A water wave on a lake has a wavelength of 15 cm and a frequency of 20 Hz. What is the wave’s speed? A wave has a speed of 25 m/s and a wavelength of 8.0 m. Want is its period?