Chapter 9: Introduction To Waves



Chapter 9:  Introduction To Waves

In this chapter we will have a group project.

 

Vocabulary:

Wave                                                    Medium

Mechanical Wave                            Transverse Wave

Longitudinal Wave                           Crest

Trough                                                  Compression    

Rarefaction                                         Wavelength

Frequency                                          Period

Amplitude                                           Refraction

Diffraction                                           Interference

Standing Wave                                  Node

Resonance

 

Section 1: The nature of waves

 

A wave is a repeating disturbance that transfers energy through matter or space.

Examples: Ocean waves, Sound waves, Seismic waves and Light waves.

 

Waves transfer energy  as they move, however the actual matter is not moved.

 

Think of a boat in the water, a wave can hit it and the boat will move up and down with the wave, however, after the wave passes, the boat is essentially in the same place.

 

All waves, no matter the type, have this property, they carry energy without transporting matter from place to place.

 

Making Waves

A wave will travel only as long as it has energy to carry.

Eventually the energy is gradually transferred to the surrounding wind and air, at the same time, the remaining energy in the waves spreads out as the waves spread out.

As the energy spreads out and is transferred away from the waves, the waves shrink and disappear.

Slinky

 

Mechanical Waves

A Medium is matter through which a wave travels. It can be air, or water or a solid.

 

Not all waves need a medium to travel. Light and radio waves can travel through a vacuum without a medium.

Waves that can travel only through matter, like sound waves, are called Mechanical Waves.

 

Mechanical waves are separated into two categories, transverse waves and longitudinal waves.

 

Transverse waves-

In a transverse wave, particles in the medium move back and forth at right angles to the direction that the wave travels.

(the particles move up and down as the wave moves across)

Water waves are an example of this.

 

 

Longitudinal waves-

In a longitudinal wave, matter in the medium moves back and forth along the same direction that the wave travels.

(coils of the slinky)

Sound waves are an example of this.

 

Section 2: Wave Properties

 

Parts of a wave

Waves can differ in how much energy they carry and how fast they travel, as well as what type they are. Waves also have other characteristics that make them different from each other.

 

Let’s look first at transverse waves-

 

 

 

The transverse wave above has alternating high and low points.

Crests are the high points of a transverse wave.

Troughs are low points of a transverse wave.

The imaginary line that is half of the vertical distance between the crest and trough is called the rest position.

Label the parts of the transverse wave:

 

 

 

 

 

Now look at a longitudinal wave-

 

 

 

 

the longitudinal wave has alternating dense and sparse regions

Compression is the more dense region of a longitudinal wave.

Rarefaction is the less-dense region of a longitudinal wave.

 

Label the parts of the longitudinal wave:

 

 

 

 

 

 

Wavelength

All waves, no matter the type, have a wavelength.

Wavelength  is the distance between one point on a wave and the nearest point just like it.

On a transverse wave, wave length is from crest to crest.

On a longitudinal wave, a wavelength is the distance from the middle of one compression to the middle of the next one.

Label the wavelengths:

 

 

 

 

 

 

 

 

Frequency and Period

Frequency is the number of wavelengths that pass a fixed point each second.

You can find the frequency of a transverse wave by counting the number of crests that pass by a point each second.

On a longitudinal wave you count the number of compressions that pass a point each second.

Frequency is expressed in hertz (Hz). 1 Hz means that one wavelength passes in 1 second.

 

The period of a wave is the amount of time it takes one wavelength to pass a point.

The period has a unit of seconds.

 

 

As the frequency increases, the period decreases.

Frequency ^       Period v

 

 

Wavelength and frequency are also related.

As the wavelength decreases, the frequency increases.

Wavelength v                    Frequency ^

 

 

 

Using these relationships we can find the wave speeds

 

Speed = frequency x wavelength

(m/s) = Hz x m

 

V=f λ

 

 

Practice:

What is the Wave speed if the wavelength is 2.0 m and the frequency is 170.5 Hz?

 

 

 

 

341 m/s

 

 

A wave traveling in water has a frequency of 250 Hz and a wavelength of 6.0 m. What is its speed?

 

 

 

 

A wave has a speed of 340 m/s and a frequency of 20 Hz, what is the wavelength?

 

 

 

 

 

A wave is broadcast at 100,000,000 Hz, and a speed of 300,000,000 m/s. What is the wavelength?

 

 

 

 

 

 

 

Amplitude

The amplitude is a measure of the size of the disturbance from the wave.

The greater the amplitude the greater the disturbance from the wave- think of an earthquake.

 

 

The amplitude of the longitudinal wave is related to how tightly the medium is pushed together at the compressions and how much the medium is pulled apart at the rarefactions.

 

The more tightly pushed together at the compressions, the denser the medium. The denser the medium the larger the amplitude.

 

 

 

The amplitude of transverse waves is the vertical distance from the crest to the rest position of the wave.

 

Label the amplitude on a transverse wave:

Section 3: The Behavior of Waves

Reflection

echoes that you hear, and images you see in windows or mirrors are caused by wave reflection.

Reflection occurs when a wave strikes an object and bounces off of it.

All types of waves can be reflected.

the law of reflection

the angle of incidence is always equal to the angle of reflection.

Refraction is the bending of a wave caused by a change in its speed as it travels from one medium to another.

the greater the change in speed the more the wave bends.

when the wave slows down it bends toward the normal line, when it speeds up it bends away from the normal line.

see figure 15 p 288

refraction is what makes a straw in a glass look broken. it makes fish look closer to the surface.

Diffraction is the bending of a wave around an object.

(think of waves moving around a rock in the ocean)

waves can also be diffracted when they pass through a narrow opening.

the amount of diffraction that occurs depends on how big the obsticle or opening is compared with the wavelength.

Interference is the process of two or more waves overlapping and combining to form a new wave.

the new wave exists only while the two original waves continue to overlap.

the waves can combine through constructive or destructive interference.

Constructive interference- the waves add together--the crests of the waves arrive at the same time and overlap, making a larger wave.

Destructive interference- the waves subtract from each other-- the crest of one wave falls at the same time as the trough from the other, making a smaller wave.

standing wave is a special type of wave pattern that occurs when waves equal in wavelength and amplitude but traveling in opposite directions continuously interfere with each other.

nodes locations in a standing wave where the interfering waves always cancel

resonance is the process by which an object is made to vibrate by absorbing energy at its natural frequencies

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