Chapter 11Section 3 Properties of waves

Objectives

Distinguish local particle vibrations from overall wave motion.

Differentiate between pulse waves and periodic waves.

Interpret waveforms of transverse and longitudinal waves.

Apply the relationship among wave speed, frequency, and wavelength to solve problems.

Relate energy and amplitude.

Waves

Waves are everywhere. Whether we recognize it or not, we encounter waves on a daily basis. Sound waves, visible light waves, radio waves, microwaves, water waves, sine waves, cosine waves, stadium waves, earthquake waves, waves on a string, and slinky waves and are just a few of the examples of our daily encounters with waves. In addition to waves, there are a variety of phenomena in our physical world that resemble waves so closely that we can describe such phenomenon as being wavelike. The motion of a pendulum, the motion of a mass suspended by a spring, the motion of a child on a swing, and the "Hello, Good Morning!" wave of the hand can be thought of as wavelike phenomena. Waves (and wavelike phenomena) are everywhere!

What is a wave?

So waves are everywhere. But what makes a wave a wave? What characteristics, properties, or behaviors are shared by the phenomena that we typically characterize as being a wave? How can waves be described in a manner that allows us to understand their basic nature and qualities?

A wave can be described as a disturbance that travels through a medium from one location to another location. Consider a slinky wave as an example of a wave. When the slinky is stretched from end to end and is held at rest, it assumes a natural position known as the equilibrium or rest position.

A wave is the motion of a disturbance.

What is a medium?

But what is meant by the word medium? A medium is a substance or material that carries the wave. You have perhaps heard of the phrase news media. The news media refers to the various institutions (newspaper offices, television stations, radio stations, etc.) within our society that carry the news from one location to another. The news moves through the media. The media doesn't make the news and the media isn't the same as the news. The news media is merely the thing that carries the news from its source to various locations. In a similar manner, a wave medium is the substance that carries a wave (or disturbance) from one location to another. The wave medium is not the wave and it doesn't make the wave; it merely carries or transports the wave from its source to other locations.

Types of waves

Waves that require a medium through which to travel are called mechanical waves. Water waves and sound waves are mechanical waves.

Electromagnetic waves such as visible light do not require a medium.

Types of waves

Waves come in many shapes and forms. While all waves share some basic characteristic properties and behaviors, some waves can be distinguished from others based on some observable (and some non-observable) characteristics. It is common to categorize waves based on these distinguishing characteristics.

Types of waves

A wave that consists of a single traveling pulse is called a pulse wave.

Whenever the source of a wave’s motion is a periodic motion, such as the motion of your hand moving up and down repeatedly, a periodic wave is produced.

A wave whose source vibrates with simple harmonic motion is called a sine wave. Thus, a sine wave is a special case of a periodic wave in which the periodic motion is simple harmonic.

Types

A transverse wave is a wave in which particles of the medium move in a direction perpendicular to the direction that the wave moves. Suppose that a slinky is stretched out in a horizontal direction across the classroom and that a pulse is introduced into the slinky on the left end by vibrating the first coil up and down. Energy will begin to be transported through the slinky from left to right. As the energy is transported from left to right, the individual coils of the medium will be displaced upwards and downwards. In this case, the particles of the medium move perpendicular to the direction that the pulse moves. This type of wave is a transverse wave. Transverse waves are always characterized by particle motion being perpendicular to wave motion.

Types of waves

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longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction that the wave moves. Suppose that a slinky is stretched out in a horizontal direction across the classroom and that a pulse is introduced into the slinky on the left end by vibrating the first coil left and right. Energy will begin to be transported through the slinky from left to right. As the energy is transported from left to right, the individual coils of the medium will be displaced leftwards and rightwards. In this case, the particles of the medium move parallel to the direction that the pulse moves. This type of wave is a longitudinal wave. Longitudinal waves are always characterized by particle motion being parallel to wave motion.

types

Definitions

Crest: is the highest point above the equilibrium position

Trough: Is the lowest point below the equilibrium position

Wavelength: Is the distance between two adjacent similar points of a wave, such as from crest to crest or from trough to trough

Definitions

Period, frequency and wave speed

The frequency of a wave describes the number of waves that pass a given point in a unit of time.

The period of a wave describes the time it takes for a complete wavelength to pass a given point.

The relationship between period and frequency in SHM holds true for waves as well; the period of a wave is inversely related to its frequency.

Period, frequency and wave speed

The speed of a mechanical wave is constant for any given medium.

The speed of a wave is given by the following equation:

v = fwave speed = frequency wavelength

This equation applies to both mechanical and electromagnetic waves.

Example#1

A piano string tuned to middle c vibrates with a frequency of 262 Hz. Assuming the speed of sound in air is 343 m/s, find the wavelength of the sound wave produce by the string.

Example#2

ruby-throated hummingbird beats its wings at a rate of about 70 wing beats per second.

a. What is the frequency in Hertz of the sound wave?

b. Assuming the sound wave moves with a velocity of 350 m/s, what is the wavelength of the wave?

 

solution

Waves transfer energy

Waves transfer energy by the vibration of matter.

Waves are often able to transport energy efficiently.

The rate at which a wave transfers energy depends on the amplitude. › The greater the amplitude, the more energy a wave

carries in a given time interval. › For a mechanical wave, the energy transferred is

proportional to the square of the wave’s amplitude. The amplitude of a wave gradually diminishes

over time as its energy is dissipated.

Homework

Do problems 1-3 in your book page 383

Today we learned about the properties of waves

Next class we are going to have a lab