Chapter Twelve Waves

Chapter 23.2 Learning Goals Describe the properties and behavior of waves. Calculate the speed of waves. Identify the parts of a wave.

Natural Frequency and Resonance Key Question: What is resonance and why is it important?

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.

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

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

Energy of Waves The energy of a wave is dependent on the frequency, period and amplitude of the wave. Energy increases when Frequency increases, Period decreases, or Amplitude increases.

Types of Waves Transverse Waves: Oscillations move perpendicular to the motion of the wave. Oscillation Particle Motion Direction of Wave

Transverse Waves

Types of Waves Longitudinal Waves: Oscillations move parallel to the motion of the wave. Particle Motion Oscillation Direction of Wave

Longitudinal Waves

Wave Demo!!

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.

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

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

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. We use l (lambda) to represent wavelength.

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?

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.

The speed of waves The speed is distance traveled divided by time. Distance is equal to wavelength. Time is equal to the period. Speed = Distance = Wavelength Time Period Since Period is 1/frequency, we can replace them. Speed = Wavelength x Frequency v =  · f

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.

Solving Problems Looking for: Given Relationships: Solution …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 = 0.2 s

Solving Problems The musical note A above middle C has a frequency of 440 Hz. If the speed of sound is known to be 331 m/s, what is the wave length of this note? You are given: f = 440 Hz v = 331 m/s 1. Write the Equation v = f x λ 2. Rearrange for value λ = v/f 3. Plug in known values to solve λ = (331 m/s)/(440 Hz) λ = 0.80 meters

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

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

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.

Resonance Everything has a natural frequency that it can make it oscillate. Examples: Jump Rope When it is moved correctly, it can be used for jumping. When it is moved incorrectly, it fluctuates, but cannot be used for jumping. Swing Pushes are synchronized so that a push is applied when the swing is up, and the swing begins to move higher.

Standing waves A wave that is confined in a space is called a standing wave. A string with a standing wave is a kind of oscillator.

24.2 Standing waves The place on a harmonic with the greatest amplitude is the antinode. The place where the string does not move (least amplitude) is called a node.

24.2 Standing waves It is easy to measure the wavelength of a standing wave on a string.

Wave Interference When two or more waves come in contact with each other, they interfere with each other. Constructive interference happens when waves add up to make a larger amplitude. Occurs when the waves are “in phase.” Destructive interference happens when waves add up to make a smaller amplitude. Occurs when the waves are “out of phase.”