Waves Chapter 25

Waves Waves are everywhere. Sound waves, light waves, water waves, stadium waves, earthquake waves, waves on a string, and slinky waves and are just a few of the examples of waves. Waves are an energy transport phenomenon, a way to transport energy from one location to another. Waves are a disturbance that travels through a medium from one location to another; a wiggle in space and time. The medium is a substance or material that carries the wave. Waves are caused by vibrations A vibration (or oscillation) is a back-and-forth or up-and-down motion; a wiggle in time.

Types of Waves We will discuss two types of waves longitudinal (or compression) and transverse Transverse wave - oscillations are transverse (perpendicular) to the direction of motion Longitudinal (or Compression) wave - oscillations are in the direction of motion or parallel to the direction of motion.

Anatomy of a Wave The parts of a wave include crest, trough, wavelength, amplitude, frequency and period crest trough The points A and F are called the CRESTS of the wave. The points D and I are called the TROUGHS of the wave. This is the point where the wave exhibits the maximum amount of positive or upwards displacement These are the points where the wave exhibits its maximum negative or downward displacement.

Anatomy of a Wave The distance between the dashed line and point A is called the amplitude of the wave. The amplitude is the maximum displacement that the wave moves away from its equilibrium. The distance between two consecutive similar points (in this case two crests) is called the wavelength. The wavelength is also the length of the wave pulse. Wavelength Wavelength Amplitude Wavelength

Wave Frequency and Period Frequency measure how often something happens over a certain amount of time (# of waves/second) We can measure how many times a pulse passes a fixed point over a given amount of time, and this will give us the frequency. The period (T) is the time it takes for one cycle (wave) to complete. The period is also is the reciprocal of the frequency. T = 1 / f f = 1 / T

The Period of a Pendulum The motion of a pendulum and the motion of a mass on a spring can be described using a wave. The period of a pendulum is the time is takes for one full back and forth motion.

Wave Speed Wave speed is the distance the disturbance travels in a fixed amount of time. Wave speed can be determined from the product of the wavelength and the frequency velocity = wavelength x frequency v = f This equation is known as the wave equation

Wave Questions Rhonda sends a pulse along a rope. How does the position of a point on the rope, before the pulse comes, compare to the position after the pulse has passed? Why don't incoming ocean waves bring more water on to the shore until the beach is completely submerged? In order for a medium to be able to support a wave, the particles in the wave must be a) frictionless. b) isolated from one another. c) able to interact. d) very light. A transverse wave is transporting energy from east to west. How will the particles of the medium will move? A wave is transporting energy from left to right. The particles of the medium are moving back and forth in a leftward and rightward direction. This type of wave is known as a _______________.

More Wave Questions 6) In the diagram above, the wavelength is given by what letter? 7) In the diagram above, the amplitude is given by what letter? 8) A wave has an amplitude of 2 cm and a frequency of 12 Hz, and the distance from a crest to the nearest trough is measured to be 5 cm. Determine the period of such a wave. 9) A tennis coach paces back and forth along the sideline 10 times in 2 minutes. The frequency of her pacing is ________. 10) A pendulum makes 40 vibrations in 20 seconds. Calculate its period? 11) Mac and Tosh are resting on top of the water near the end of the pool when Mac creates a surface wave. The wave travels the length of the pool and back in 25 seconds. The pool is 25 meters long. Determine the speed of the wave. 12) A marine weather station reports waves along the shore that are 2 meters high, 8 meters long, and reach the station 8 seconds apart. Determine the frequency and the speed of these waves.

Wave Behavior Now the we know the parts of a wave and how we describe and analyze them, we can look at wave behavior In the next section we will look at interference, the boundary behavior of waves, standing waves and the Doppler Effect. The Doppler Effect

The Doppler Effect The Doppler Effect is the apparent change in frequency of a wave due to relative motion between source and observer. As the sound move toward the observer, the apparent frequency decreases, the waves get compressed. As the sound moves away from the observer, the apparent frequency increases, the waves get “stretched out” A sound wave frequency change is noticed as a change in pitch.

Doppler Shift for Light

Doppler and Line of Sight We are only sensitive to motion between source and observer ALONG the line of sight.

Interference and the Superposition Principle Suppose two waves pass through the same medium. What happens? Wave interference is the phenomenon which occurs when two or more waves meet while traveling along the same medium. The superposition principle tells us how waves interact. The principle of superposition is sometimes stated as follows: When two waves interfere, the resulting displacement of the medium at any location is the algebraic sum of the displacements of the individual waves at that same location. Algebraic sum of two waves

Constructive Interference Constructive interference is a type of interference which occurs at any location along the medium where the two interfering waves have a displacement in the same direction. The resulting displacement is greater than the displacement of the two interfering pulses alone.

Wave Addition

Destructive Interference Destructive interference is a type of interference which occurs at any location along the medium where the two interfering waves have a displacement in the opposite direction. The resulting displacement is less than the displacement of the two interfering pulses alone.

Wave Subtraction

Two Opposite Waves When the two opposite waves arrive at the same location, they cancel, destructively.

Interference Water waves from two oscillating sources Computer Simulation Ripple Tank

Boundary Behavior of Waves The behavior of a wave when it reaches the end of its medium is called the wave’s boundary behavior. When one medium ends and another begins, that is called a boundary. One type of boundary that a wave may encounter is that it may be attached to a fixed end. The reflected pulse has the same speed, wavelength, and amplitude as the incident pulse.

Standing Waves When a reflected wave interferes with an incident wave, a standing wave can form. Nodes are points of no motion Anti-nodes are points of maximum motion

Harmonics There are a variety of patterns by which the guitar string could naturally vibrate; each pattern is associated with one of the natural frequencies of the guitar strings.

Sources Conceptual Physics by Paul Hewitt www.physicsclassroom.com pls.atu.edu/physci/physics/people/robertson/courses/phsc1013/PHSC1013-Waves.ppt – Waves and Vibrations -Physics: Mr. Maloney