Chapter 12 The Nature of Waves

After completion of this section, you should be able to: Demonstrate your understanding of categorizing waves. Define, relate and apply the concepts of frequency, wavelength, and wave speed. Solve problems involving mass, length, tension, and wave velocity for transverse waves. Write and apply an expression for determining the characteristic frequencies for a vibrating string with fixed endpoints.

Categorizing Waves I Waves categorized on the basis of the direction of movement of the individual particles of the medium relative to the direction which the waves travel..

Categorizing waves on this basis leads to three categories: a. transverse waves, b. longitudinal waves, c. and surface waves.

Transverse Wave transverse wave is a wave in which particles of the medium move in a direction perpendicular to the direction which the wave moves.

Transverse Wave The particles do not move along with the wave; they simply oscillate up and down about their individual equilibrium positions as the wave passes by. Pick a single particle and watch its motion.

A Transverse Wave In a transverse wave, the vibration of the individual particles of the medium is perpendicular to the direction of wave propagation. Motion of particles Motion of wave

Parts of a Transverse Wave Crest Trough Amplitude Wavelength

Crest and Trough Crest – the point on the medium which exhibits the maximum amount of positive or upwards displacement from the rest position. Trough – the point on the medium which exhibits the maximum amount of negative or downwards displacement from the rest position

Wavelength Measured in meter Length of one complete wave cycle

Amplitude maximum amount of displacement of a a particle on the medium from its rest position normal

Longitudinal Wave longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction which the wave moves Ex. - sound wave

Longitudinal Waves In a longitudinal wave, the vibration of the individual particles is parallel to the direction of wave propagation. v Motion of particles Motion of wave

Longitudinal Wave In a longitudinal wave the particle displacement is parallel to the direction of wave propagation. The particles do not move down the tube with the wave; they simply oscillate back and forth about their individual equilibrium positions. Pick a single particle and watch its motion

Longitudinal Waves Compression - a point on a medium through which a longitudinal wave is traveling which has the maximum density. Rarefaction is a point on a medium through which a longitudinal wave is traveling which has the minimum density.

Surface Wave surface wave is a wave in which particles of the medium undergo a circular motion. Surface waves are neither longitudinal nor transverse. Two types of surface waves: a. Love Waves b. Rayleigh Waves

The arrow shows the direction that the wave is moving. Love Waves the fastest surface wave and moves the ground from side-to-side.

Rayleigh Waves A Rayleigh wave rolls along the ground just like a wave rolls across a lake or an ocean. Because it rolls, it moves the ground up and down, and side-to-side in the same direction that the wave is moving. Most of the shaking felt from an earthquake is due to the Rayleigh wave, which can be much larger than the other waves.

Most of the shaking felt from an earthquake is due to the Rayleigh wave, which can be much larger than the other waves.

Categorizing Waves II Another way to categorize waves is on the basis of the ability to transmit energy through a vacuum a. mechanical waves b. electromagnetic waves.

Mechanical Waves A mechanical wave is a physical disturbance in an elastic medium. Consider a stone dropped into a lake. Energy is transferred from stone to floating log, but only the disturbance travels. Actual motion of any individual water particle is small. Energy propagation via such a disturbance is known as mechanical wave motion.

Electromechanical Waves We will get to later…

Wave Change Waves may demonstrate: Reflection Refraction Diffusion

Reflection With a free boundary, waves are reflected With a fixed boundary, waves are reflected and inverted

Velocity and Wave Frequency. The period T is the time to move a distance of one wavelength. Therefore, the wave speed is: The frequency f is in s-1 or hertz (Hz). The velocity of any wave is the product of the frequency and the wavelength:

Example: An electromagnetic machine sends waves down a string Example: An electromagnetic machine sends waves down a string. The machine makes 600 complete cycles in 5 s. For one complete vibration, the wave moves a distance of 20 cm. What are the frequency, wavelength, and velocity of the wave? f = 120 Hz The distance moved during a time of one cycle is the wavelength; therefore: v = fl v = (120 Hz)(0.02 m) l = 0.020 m v = 2.40 m/s

Summary for Wave Motion: