physics ii - waves

8/6/2019 Physics II - Waves

1/15

OSCILLATIONS AND WAVES


2/15

Oscillations can cause waves. The world is full ofwaves: sound waves, waves on a string, earthquakewaves, and electromagnetic waves.

Waves are oscillations that carry energy from one placeto another, yet matter is not carried with the wave.

Analogy: Setting up dominoes and knocking them down illustrates

this. Each domino moves very little, but the energy maymove over a long distance.

If you watch a leaf or a cork on a lake as waves move by it,the leaf or cork moves very little, but the wave moves along ways. Waves may move in one, two or three

dimensions. A wave pulse on a rope basically moves in one

dimension. Water waves on a lake move in twodimensions, and spoken sound waves spread out in threedimensions.


3/15

Mechanical waves have two general

characteristics:

A disturbance is in some identifiable medium.

Energy is transmitted from place to place, butthe medium does not travel between two places.


4/15

Mechanical waves Most familiar - Eg: water waves, sound waves

Governed by Newtons law

Exist only within a material medium suc as water,

air and rock Electromagnetic waves

Less familiar

Eg: ultraviolet light, radio & television waves,microwaves, x rays, radar waves

Require no material medium to exist

Matter waves Unfamiliar

Eg: electrons, protons, atoms, molecules


5/15

There are two basic types of waves: transverse waves

longitudinal waves

Each type of wave describes the motion of a small

segment of the wave. In a transverse wave, each segment moves

perpendicular or transverse to the direction of motion

of the wave.

Eg: A rope with a pulse on it.

In a longitudinal wave, each segment moves along

the direction of the the motion of the wave.

Eg: A spring or slinky which is quickly compressed, then

returned to its original position.


6/15

The left side of Figure 1: A pulse travels on a string. As the pulse

passes point Pon the string, the point moves up and then back to the

equilibrium position. Each segment of the rope moves onlyperpendicular to the motion of the wave.

The right side of Figure 1: The pulse propagated along a stretched

spring. The individual points along the medium (the spring) travel

back and forth parallel to the motion of the pulse. Eg: Sound waves.


7/15

Important basic characteristics of waves:wavelength,amplitude,period, and

frequency.

Wavelength is the length of the repeating

wave shape. Amplitude is the maximum displacement of

the particles of the medium, which is

determined by the energy of the wave.

Figure 2 illustrates the wavelength (representedby the Greek letter lambda) and the amplitude

(byA) for both transverse and longitudinalwaves.


8/15


9/15

The period ( T) is the time for one wave to passa given point. Period is measured in seconds.

Frequency of the wave (f) is the number ofwaves passing a given point in a unit of time. Frequency is measured in cycles per second or the SI

unit of hertz (Hz) with the dimensions of sec1. For example: a wave generated at 60 cycles per

second has a frequency of 60 Hz and can be expressedas 60/s.

Frequency is the reciprocal of the period:f= I / T


10/15

From the definition of velocity as distance/time

(distance divided by time)for all types of wavesthe velocity is given by the following:

Frequency is the reciprocal of period,

velocity:

v = f

The velocity is dependent upon thecharacteristics of the medium carrying the

wave.


11/15

Example 1

A person on a pier observes a set of incoming

waves that have a sinusoidal form with a

distance of 1.6 m between the crests. If a

wave laps against the pier every 4.0 s, whatare

a) The frequency

b) The speed of the waves


12/15

SUPERPOSITION PRINCIPLE

If two waves pass through the same region of space, theycombine by a process called superposition.

The superpositionprinciple: The resultant wave formedby the simultaneous influence of two or more waves is thevector sum of the displacements due to each wave actingindependently.

As shown in Figure 3(a), if two pulses of the same size andshape on the same side of the rope arrive at a given pointat the same time, they willfor an instantcombine toform a pulse that is twice the size of each of the individual

pulses. This is called constructiveinterference. Figure 3(b) shows what happens if the same two pulses are

on opposite sides of the string. In this case, the two pulseswill momentarily cancel each other out. This is calleddestructiveinterference.


13/15

There are two waves approaching each other on the same

string, they will interfere with each other.

If they both have a positive amplitude, they will interfereconstructively, and the resultant wave will have a largeramplitude. If one wave has a positive amplitude and one has a negativeamplitude, they will interfere destructively,and the resultant

wave will have a smaller amplitude.


14/15

When a wave encounters an obstacle, theybend around the obstacle. This is calleddiffraction.

The amount of bending depends on the sizeof the wavelength and the size of theobject.

It is diffraction that allows us to hear soundseven when the source is not directly in line

with us. For instance, if you go around a corner and talk,

your friend can still here you because the wavesare bent around the obstacle, which is the wall.


15/15

When a wave travels from one medium to

another, (like from air to water), part of the

wave is reflected and part continues into the

medium and is transmitted.

The part that is transmitted will often move in a

different direction from the original wave. This

phenomenon is called refraction. The wave is refracted because it changes

velocity in the new medium. See figure 11-36

which shows how wave fronts will change

direction if they move at a different velocity.

physics ii - waves

Documents