Chapter Twenty-Three: Waves 23.1 Harmonic Motion 23.2 Properties of Waves 23.3 Wave Motion

23.1 Harmonic motion Linear motion gets us from one place to another. Harmonic motion is motion that repeats over and over.

23.1 Harmonic motion A pendulum is a device that swings back and force. A cycle is one unit of harmonic motion.

23.1 Oscillators An oscillator is a physical system that has repeating cycles or harmonic motion. Systems that oscillate move back and forth around a center or equilibrium position.

23.1 Oscillators A restoring force is any force that always acts to pull a system back toward equilibrium.

23.1 Harmonic motion Harmonic motion can be fast or slow, but speed constantly changes during its cycle. We use period and frequency to describe how quickly cycles repeat themselves. The time for one cycle to occur is called a period.

23.1 Harmonic motion The frequency is the number of complete cycles per second. Frequency and period are inversely related. One cycle per second is called a hertz, abbreviated (Hz).

The period of an oscillator is 2 minutes. Solving Problems The period of an oscillator is 2 minutes. What is the frequency of this oscillator in hertz?

Looking for: Given Relationships: Solution f = .008 Hz Solving Problems Looking for: …frequency in hertz Given …period = 2 min Relationships: …60 s = 1 min … f = 1/T Solution … f = 1/120 s f = .008 Hz

23.1 Amplitude Amplitude describes the “size” of a cycle. The amplitude is the maximum distance the oscillator moves away from its equilibrium position.

23.1 Amplitude The amplitude of a water wave is found by measuring the distance between the highest and lowest points on the wave. The amplitude is half this distance.

23.1 Amplitude A pendulum with an amplitude of 20 degrees swings 20 degrees away from the center in either direction.

23.1 Damping Friction slows a pendulum down, just as it slows all motion. Damping is the gradual loss of amplitude.

23.1 Graphs of harmonic motion A graph is a good way to show harmonic motion because you can quickly recognize cycles. Graphs of linear motion do not show cycles.

23.1 Natural frequency and resonance The natural frequency is the frequency (or period) at which a system naturally oscillates. Every system that oscillates has a natural frequency.

23.1 Natural frequency and resonance You can get a swing moving by pushing it at the right time every cycle. A force that is repeated over and over is called a periodic force.

23.1 Natural frequency and resonance Resonance happens when a periodic force has the same frequency as the natural frequency. When each push adds to the next one, the amplitude of the motion grows.

23.2 Waves A wave is an oscillation that travels from one place to another. If you poke a floating ball, it oscillates up and down. The oscillation spreads outward from where it started.

23.2 Waves When you drop a ball into water, some of the water is pushed aside and raised by the ball.

23.2 Waves Waves are a traveling form of energy because they can change motion. Waves also carry information, such as sound, pictures, or even numbers.

23.2 Frequency, amplitude, and wavelength You can think of a wave as a moving series of high points and low points. A crest is the high point of the wave. A trough is the low point.

23.2 Frequency The frequency of a wave is the rate at which every point on the wave moves up and down. Frequency means “how often”.

23.2 Amplitude The amplitude of a water wave is the maximum height the wave rises above the level surface.

23.2 Wavelength Wavelength is the distance from any point on a wave to the same point on the next cycle of the wave. The distance between one crest and the next crest is a wavelength.

23.2 The speed of waves The speed of a water wave is how fast the wave spreads, NOT how fast the water surface moves up and down or how fast the dropped ball moves in the water. How do we measure the wave speed?

23.2 The speed of waves A wave moves one wavelength in each cycle. Since a cycle takes one period, the speed of the wave is the wavelength divided by the period.

23.2 The speed of waves The speed is the distance traveled (one wavelength) divided by the time it takes (one period). We usually calculate the speed of a wave by multiplying wavelength by frequency.

Calculate the frequency and the period of the wave. Solving Problems The wavelength of a wave on a string is 1 meter and its speed is 5 m/s. Calculate the frequency and the period of the wave.

f = 5 Hz T = .2 s Solving Problems Looking for: Given Relationships: …frequency in hertz …period in seconds Given … = 1 m; s = 5 m/s Relationships: s = f x  or f = s ÷  f = 1/T or T = 1/f Solution f = 5 m/s ÷1 m = 5 cycles/s T = 1/5 cycles/s = .2 s f = 5 Hz T = .2 s

23.3 Wave Motion A wave front is the leading edge of a moving wave which is considered to be the crest for purposes of modeling. The crests of a plane wave look like parallel lines. The crests of a circular wave are circles.

23.3 Four wave interactions When a wave encounters a surface, four interactions can occur: reflection, refraction, diffraction, or absorption.

23.3 Wave interactions A boundary is an edge or surface where things change. Reflection, refraction, and diffraction usually occur at boundaries.

23.3 Wave interactions Diffraction usually changes the direction and shape of the wave. When a plane wave passes through a small hole diffraction turns it into a circular wave.

23.3 Transverse and longitudinal waves A wave pulse is a short ‘burst’ of a traveling wave. It is sometimes easier to see the motion of wave pulses than it is to see long waves with many oscillations.

23.3 Transverse waves The oscillations of a transverse wave are not in the direction the wave moves.

23.3 Longitudinal waves The oscillations of a longitudinal wave are in the same direction that the wave moves.

23.3 Constructive interference Constructive interference happens when waves add up to make a larger amplitude. Suppose you make two wave pulses on a stretched string. One comes from the left and the other comes from the right. When the waves meet, they combine to make a single large pulse.

23.3 Destructive interference What happens when one pulse is on top of the string and the other is on the bottom? When the pulses meet in the middle, they cancel each other out. During destructive interference, waves add up to make a wave with smaller or zero amplitude.