DAY 17

 

Summary of Topics Covered in Today’s Lecture

NOTE – THIS PAGE USES A LOT OF ANIMATION, AND CONTAINS SEVEL SUB-PAGES. 

IT WILL NOT PRINT VERY WELL.

 

Wave Basics

 

Waves are a net movement of energy without an accompanying net movement of matter.  While waves can come in many shapes, the most important kind of wave is a sinusoidal traveling wave of the form

 

 

 

or

 

 

 

bd10264_ Click here for discussion of Amplitude (A).

bd10264_ Click here for discussion of Wavelength (l).

bd10264_ Click here for discussion of Frequency (f).

bd10264_ Click here for discussion of Phase angle (f).

 

Since a wave moves a distance of one wavelength in a time of one period, the speed of a wave is given by

 

 

Most waves require a medium through which to travel.  For instance, sound waves must travel through a medium such as air or water; sound cannot travel through a vacuum. 

 

Waves in which the direction of oscillation of the medium is parallel to the wave’s motion are called longitudinal waves.  Sound waves are longitudinal waves.  The animation at right showns the motion of air around a tuning fork.  The waves travel radially outward from the source, and the oscillation of the air is along the same line of motion.

longquad

http://www.kettering.edu/~drussell/Demos/rad2/mdq.html

 

Waves in which the direction of oscillation of the medium is perpendicular to the wave’s motion are said to be transverse waves.  Water waves, and the waves in the demo programs you saw above are transverse waves.  Usually when we make a diagram of a wave we draw a transverse wave. 

 

The animations below compare longitudinal and transverse waves.  In both cases the waves move to the right, while the individual particles oscillated in place.  In the longitudinal wave the particles oscillate left-right, while in the transverse wave the particles oscillate up-down.

Lwave.gif

Longitudinal wave
Follow one wave with your eye and watch it move to the right.
Focus on one particle and watch it move left-right.

 

Twave.gif

Transverse wave
Follow one wave with your eye and watch it move to the right.
Focus on one particle and watch it move up-down.

 

http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html

 

 

 

Superposition and its Ramifications

 

The principle of Superposition says that when two waves are in the same place at the same time, the amplitude of the waves simply adds up directly.  In other words, the result when f(x,t) and g(x,t) meet at the same place at the same time is simply

 

y(x,t) = f(x,t) + g(x,t)

 

Furthermore, the waves maintain their identity – once they pass through one another they return to their original amplitude and continue on their merry way as though nothing had happened.

 

There are many implications to this.

 

bd10264_ Click here for more on Superposition.

bd10264_ Click here for discussion of Interference.

bd10264_ Click here for discussion of Complex Wave Forms and Fourier Synthesis.

 

Example Problem #1

 

Sound travels at roughly 340 m/s.  Find the period and wavelength of a 1000 Hz sound wave.

 

Solution:

 

v = f l

340 m/s = 1000 Hz l

(340 m/s)/(1000 1/s) = l

.340 m = l

 

T = 1/f

T = 1/1000 Hz = .001 sec

 

Period 1 ms.  Wavelength 34 cm.