Waves Chapter 25

What is a Wave? We have measured objects moving in straight lines, in circular paths, falling to the Earth and now objects that move back and forth (oscillate). A disturbance in a medium (such as air, rocks, etc.) causes a vibration (a back and forth motion), this in turn creates a wave. A wave is a vibration that can be measured with time and distance.

Pendulums and Waves In science we liked to use a pendulum (a string with a weight on it that can swing back and forth) to represent the basic characteristics of a wave. When you time one back and forth motion you have determined the period of one wave vibration.

Period of a Wave The period of a wave is only dependent on the length of the pendulum (Which you will see later, represents the wavelength of a wave and affects the frequency of that wave) and the acceleration of gravity. (Since the pendulum swings downward and upward it is affected by gravity, this in turn affects the wave frequency on a pendulum). The frequency of a wave will be discussed in further sections. Refer back to this section to help you make the connections.

Relationships to be made The relationship between length and acceleration due to gravity and the period of a wave can be seen in the formula: T = 2π When length is increased the period of the wave represented by the capital letter (T) will increase proportionally. When the acceleration due to gravity is increased, (T) will decrease inversely.

Harmonic Motion The back and forth motion of a swinging pendulum or any simple vibration is called simple harmonic motion. Simple harmonic motion is defined as a vibration in which the restoring force (force that brings the object back to its normal position) and the displacement (height) from the normal position are proportional.

Sine Curves A wave can be traced on paper using an object that oscillates back and forth. This tracing forms a sideways (S). This is called a sine curve, it represents the crests (high points) and troughs (low points) of a wave. It also helps to understand the characteristics of waves.

Characteristics of a Wave

Frequency When you count the number of back and forth movements in a given amount of time (usually one second) you have measured a wave’s frequency. The unit for frequency is “hertz”. If you count 1 back and forth movement in a 1 second time period the frequency of the wave is 1 Hz. If you count 2 waves in 1 sec, the frequency is 2 Hz.

Frequency The source of all waves is something that vibrates. The frequency of the vibrating source and the frequency of the wave it produces are the same. (Look at figure 25.3, notice the ball on the spring. The frequency of the spring moving up and down matches the frequency of the wave it produces).

Period and Frequency If the frequency of a vibrating object is known, its period can be calculated, and vice versa. f = If you know T you can solve for f. T = If you know f you can solve for T.