isns 3371 - phenomena of nature archimedes’ principle is useful for determining the volume and...

ISNS 3371 - Phenomena of Nature

Archimedes’ principle is useful for determining the volume and therefore the density of an irregularly shaped object by measuring its mass in air and its effective mass when submerged in water.

effective mass under water = actual mass - mass of water displaced (bouyant force)

The difference between the real and effective mass therefore gives the mass of water displaced and allows the calculation of the volume of the irregularly shaped object The mass divided by the volume thus determined gives a measure of the average density of the object.

Archimedes found that the density of the king's supposedly gold crown (14.2 gr/cm3) was actually much less than the density of gold (19.3 gr/cm3) -- implying that it was either hollow or filled with a less dense substance.

440 gr/31cm3 = 14.2 gr/cm3


Waves

A wave is a pattern which is revealed by its interaction with particles. It is a vibration - a movement of particles up and down, side-to-side, or back and forth.

Waves on a Pond Animation

Wave is moving up and down but not outward - carries energy but not matter.

Sound and light are both waves - but different.

Sound is the movement of vibrations though matter - solids, liquid, or gases - no matter, no sound. Cannot travel in a vacuum.

Light is a vibration of electric and magnetic fields - pure energy - does not require matter.

ISNS 3371 - Phenomena of Nature Properties of Waves

Any traveling wave will take the form of a sine wave. The position of an object vibrating in simple harmonic motion will trace out a sine wave as a function of time. (Or if a mass on a spring is carried at constant speed across a room, it will trace out a sine wave.)

This transverse wave is typical of that caused by a small pebble dropped into a still pool.

Crest - high point of sine wave

Trough - low point of sine wave

Amplitude (a): maximum displacement from equilibrium

Wave length (l): distance between successive crests

Trough

Crest


Properties of Waves

Period: time to complete one cycle of vibration - from crest to crest or trough to trough

Frequency (f): number of crests passing a fixed pointper second

Frequency= 1/period

Example:Period = 1/100 = 0.01 sec. Frequency = 100 hertz (cycles/sec.)

Speed (of a wave) (s)= wave length x frequencys= l x f


Anatomy of a Wave Animation


Wavelength and Frequency Animation


TYPES OF WAVES

Transverse:

Vibration or oscillation is perpendicular to direction of propagation of wave.

Examples: water wave, vibrating string, light

Longitudinal:

Vibration or oscillation is in the same direction as propagation of wave.

Examples: sound waves, mass on a spring,loudspeaker


Resonant frequency - a natural frequency of vibration determined by the physical parameters of the vibrating object. This same basic idea of physically determined natural frequencies applies throughout physics in mechanics, electricity and magnetism, and even throughout the realm of modern physics.

Implications:

1. It is easy to get an object to vibrate at its resonant frequencies, hard to get it to vibrate at other frequencies.

Resonance

Consider a child's playground swing (a pendulum). It is a resonant system with only one resonant frequency. With a tiny push on the swing each time it comes back to you, you can continue to build up the amplitude of swing. If you try to force it to swing a twice that frequency, you will find it very difficult.

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/reson.html#c2


2. A vibrating object will pick out its resonant frequencies from a complex excitation and vibrate at those frequencies, essentially "filtering out" other frequencies present in the excitation.

Resonance Implications

If you just whack a mass on a spring with a stick, the initial motion may be complex, but the main response will be to bob up and down at its natural frequency. The blow with the stick is a complex excitation with many frequency components but the spring picks out its natural frequency and responds to that.


3. Most vibrating objects have multiple resonant frequencies.

Resonance Implications

An ideal vibrating string will vibrate with its fundamental frequency and all harmonics of that frequency. The fundamental vibrational mode of a stretched string is such that the wavelength is twice the length of the string.


The string will vibrate at the fundamental frequency and all harmonics of the fundamental.

Most vibrating objects have more than one resonant frequency and those used in musical instruments typically vibrate at harmonics of the fundamental.

Each of these harmonics will form a standing wave on the string. The term standing wave is often applied to a resonant mode of an extended vibrating object. Standing wave modes arise from the combination of reflection and interference.

A harmonic is defined as an integer (whole number) multiple of the fundamental frequency.

The nth harmonic = n x the fundamental frequency


The Tacoma Narrows Bridge - Resonance in Action

In 1940, the Tacoma Narrows Bridge (Galloping Gertie) was destroyed by wind-generated resonance. A strong wind generated an irregular force in resonance with the natural frequency of the bridge, increasing the magnitude of vibrations until the bridge collapsed.

QuickTime™ and a decompressor

are needed to see this picture.


Standing Wave vs Traveling Wave

Traveling wave - a type of wave pattern which is seen traveling through a medium - crests are seen to propagate through the medium

Standing wave - a wave reflected in such a way that it does not propagate.

node: point where particles are at rest.

antinode: point where particles execute maximum periodic motion, (maximum amplitude).

Standing wave modes arise from the combination of reflection and interference.


Two traveling waves which exist in the same medium will interfere with each other. If amplitudes add - constructive interference. If they are "out of phase" and subtract - destructive interference

Constructive interference is the combined result of two waves that are exactly in phase. In other words, both of the waves are operating at the exact same frequency and both of them crest at the exact same moment.

Interference

Destructive interference is the combined result of two waves that are out of phase. In other words, When the crest of one wave occurs at the same time as the trough of another wave.

ISNS 3371 - Phenomena of Nature Interference

Constructive - waves add in phase, producing larger peaks than any wave alone.

Destructive - waves add out of phase, producing smaller peaks than a single wave alone.


Interference of Waves

Dark lines are crests and light lines are troughs - interference creates a pattern.

Constructive interference occurs at A and B - crests are twice as highDestructive interference occurs at C, D, E, and F - the waves cancel out


Reflection

The string appears to vibrate in segments or regions and the fact that these vibrations are made up of traveling waves is not apparent - hence the term "standing wave".

ISNS 3371 - Phenomena of NatureProducing a Standing WaveWhen a wave of the proper frequency is produced on a string, a node occurs at the end of the string and the interference of the incident wave and the reflected wave occur in such a manner that there are specific points along the medium which appear to be standing still.

isns 3371 - phenomena of nature archimedes’ principle is useful for determining the volume and...

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