Section 14.2 Wave Properties Objectives  Identify how waves transfer energy without transferring matter.  Contrast transverse and longitudinal waves.  Relate wave speed, wavelength, and frequency.

INTRODUCTION Wave – a disturbance that carries energy through matter or space. It transfers energy without transferring matter. Newton’s laws of motion and principles of conservation of energy also govern the motion of waves. There are many kinds of waves that transmit energy, including the waves you cannot see.

MECHANICAL WAVES Water waves, sound waves, and waves that travel along a spring or rope are MECHANICAL WAVES. Mechanical wave motion requires a material medium (such as water, air, springs or ropes). Newton’s laws govern the motion of mechanical waves. Light waves, radio waves, and X rays are examples of electromagnetic waves. No medium is needed for the motion of electromagnetic waves. There is a third type of wave called the Matter wave and quantum mechanics is needed to describe it and will be discussed in Chapter 27.

MECHANICAL WAVES There are 3 different types of mechanical waves Transverse Wave Longitudinal Wave Surface Wave Wave Pulse – a single disturbance or pulse that travels through a medium. Periodic Wave – a mechanical wave that moves up and down at the same rate. Traveling Wave – a moving, periodic disturbance in a medium. You get this by moving the rope from side to side in a regular manner. Periodic Wave and Traveling Wave are the same.

MECHANICAL WAVES Transverse Wave – causes the particles of the medium to vibrate perpendicularly to the direction of motion of the wave. It is a wave in which the disturbance is perpendicular to the direction of travel of the wave. See Figure 14-5a notice the rope is displaced up and down at right angles to the motion of the wave. Examples include waves in a piano and guitar strings. Longitudinal Wave – causes the particles of a medium to move parallel to the direction of the wave. It is a wave in which the direction of the disturbance is the same as the direction of travel of the wave. See figure 14-5b notice the displacement of the spring is in the same direction of the motion of the wave. Examples include sound waves and usually fluids (liquids, gases, and plasmas) only transmit longitudinal waves. Surface Wave – a mixture of transverse and longitudinal waves. It is a wave on the surface of a liquid with characteristics of both transverse and longitudinal waves. See figure 14-6.

MEASURING A WAVE There are many ways to describe or measure a wave. Some characteristics depend on how the wave is produced, whereas others depend on the medium through which the wave travels. A wave can be measured in terms of its speed, amplitude, wavelength, phase, period and frequency. The speed of a periodic wave can be found by measuring the displacement of the wave peak, ∆d, then dividing this by the time interval, ∆t, to find the speed, given by v = ∆d/ ∆t. For most mechanical waves, both transverse and longitudinal, the speed depends only on the medium through which the waves move. Amplitude – the maximum displacement from the rest or equilibrium position.

MEASURING A WAVE A wave with a larger amplitude transfers more energy than a wave with a smaller amplitude. The larger the amplitude the greater the energy transferred. A wave’s amplitude depends on how it is generated, but not on its speed. More work must be done to generate a wave with a greater amplitude. For waves that move at the same speed, the rate at which energy is transferred is proportional to the square of the amplitude. Thus, doubling the amplitude of a wave increases the amount of energy it transfers each second by a factor of 4.

MEASURING A WAVE Crests – the high points of each wave of motion. Troughs – the low points of each wave of motion. Wavelength – distance between corresponding points on 2 successive waves. It is the shortest distance between points where the wave pattern repeats itself. From one crest to the next or one through to the next is one wavelength. It is denoted by. In Phase – when any 2 points on a wave are one or more whole wavelengths apart.

MEASURING A WAVE Particles in the medium are said to be in phase with one another when they have the same displacement from equilibrium and the same velocity. Particles in the medium with opposite displacements and velocities are 180° out of phase. Two particles in a wave can be anywhere from 0° to 180° out of phase with one another.

MEASURING A WAVE Period – time needed to repeat one complete cycle of motion. Or the shortest interval during which the motion repeats itself. It is denoted by T. It is measured in seconds. The period of a wave is equal to the period of the source. Frequency – number of occurrences per unit time. It is the number of complete vibrations per second measured at a fixed location. It is denoted by f. It is measured in Hertz (Hz). f = 1 / T Hertz – the unit for frequency. It is denoted by Hz. It is one vibration per second. Both the period and the frequency of a wave depend only on its source. They do not depend on the wave’s speed or the medium.

MEASURING A WAVE In the time interval of one period, a wave moves one wavelength. Therefore, the wavelength of a wave is the speed multiplied by the period, λ = vT. The wavelength of a wave is equal to the velocity divided by the frequency. λ = v / f or *** v = λf *** It is important to remember that while the amplitude of a mechanical wave determines the amount of energy it carries, only the medium determines the wave’s speed.

MEASURING A WAVE Example 3 p. 385 a. v = d/tb. v = λf v = 91.4 / = λ(192) v = m/s 1.76 m = λ c. f = 1 / Td. v = λf f = 1 / T 192T = = λ(442) 442T = 1 T = s.763 m = λ T = s Do Practice Problems # p. 386 Do 14.2 Section Review p. 386