Lesson 18 Waves

Oscillation can travel through mediums such as air or water without carrying water along with them. These mechanical disturbances are called waves. Waves are one of the most common natural phenomena.


Sound travels very fast but it is not infinite. Sound is a wave or disturbance that travels at a definite speed.

The "Big Bang" is an example of a wave where a disturbance in one place led to reactions in another.


When any stable mechnical system is disturbed nature's response is simple harmonic motion, where the disturbance in one place is passed on to the next as a mechanical wave.

In a crystaline solid, linkage is weak where disturbances travel slowly, and linkage is strong where disturbances travel rapidly. Any waves that propogate through a medium are mechanical waves. Impulses pass through a crystal from atom to atom because each atom is bound together to an equilibrium position by electrical forces. These atoms act mechanically like masses connected by springs.

Musical instruments send waves through the air with an amplitude the size of the disturbance which is preserved as the waves moves along. The time for each complete cycle is known as a period. The inverse of this is the frequency on which the tone of an instrument depends. The definite distance from one compression to the next is known as the wavelength.

wavelength = T v (speed of wave)

frequency x wavelength = v where speed is always the same.

In the case of water waves, speed decreases as they approach the shore. Long waves travel faster than shorter waves, however all waves obey the same principles.


Harmonic oscillations respond and spring back.

For masses on a spring:

v = a sqrt(k/m)

Gravity and the length of the water wave determine speed.

v = sqrt ( g (wavelength) / 2pi)

Masses on a spring produce waves in the direction of connection known as longitudal waves.

Waves that travel throughout a solid are known as transverse waves, however water waves are classified in neither of these categories.

Each water molecule moves on the surface in little circles where each circle is slightly offset from the next.

v = sqrt (g h) in shallow water

Waves of sound vibrate air into motion, expanding and compressing density with each vibration. This is why sound carries the same frequency as the source driven by the force that produces change in pressure as density increases and decreases. Below is a video that physically displays sound waves:



v = sqrt (pressure/density)

Newton attempted to find the speed at which sound traveled along the corridors at Trinity University and determined that the sound waves traveled at a speed of 979 ft/sec. However, Newton was incorrect and William Derham discovered that the speed of sound was in fact 1142 ft/sec. This discrepency is due to the fact that air heats up as it is compressed and travels back faster. This was not discovered until a century later.

Below is a video that explores the nature of waves in depth: