Speed of Light and Relative Speed

If Spaceman Spiff attaches a flashlight to the front of his spacecraft the light is still going to travel at the speed of light c.

Likewise if he attaches a loudspeaker to his ship in order to yell at aliens, those waves will travel at the speed of sound.

While a military plane going mach five (five times the speed of sound) could hit its own bullets, both sound and light travel at speeds independent of the source.

The plane that attains a speed of mach five will also undergo the most stress as it passes mach one since it experiences the constructive interference of the entire cone of sound at that point.

Decibels, Loudness


From woodleywonderworks on flickr

When someone returns from a heavy metal concert they don’t usually comment loudly about how many Watts per meter squared they experienced.

Decibels might make sense.  People tend to know that 120 Decibels is a lot.

This system has been devised and units of decibels measure perceived loudness.

It increases on a logarithmic scale, so something that seems twice as loud really has 10 times the intensity.

Position also can vary the perception of sound such as when a noise emitter comes nearer to you the frequency seems greater and the pitch higher (Doppler Effect).

Wave Interaction, Beats, Destructive Interference

When waves come into contact with each other they can interact together to increase or decrease amplitude.

If two sound waves are slightly off in frequency you can hear the peaks where the waves add together (constructive interference), called “beats.”

If two identical waves are off by a phase angle of pi then there will be complete destructive interference, meaning that all the energy will be cancelled while they are in contact.

Sound cancelling headphones take advantage of this property by creating waves that cancel background noise.

Wave Mediums, Bulk Modulus

Waves must be distinguished as to what medium they are traveling through, if you want to make any sense of data.

Sound will travel at a certain rate in air and another in water, and these rates can be quite different.

Materials have something called the bulk modulus which has to do with elasticity and the ease with which waves propagate through a particular substance.

Lightning goes through the air at about 1/5 mile/sec, and therefore you can count the seconds between the flash and the sound to determine how far away the lightning struck.

Temperature also affects the bulk modulus, so it should be taken into account for better precision.

Vectors, components, sine and cosine in power series

Back in algebra II or so you probably started going over vectors.

To start off, you could describe a vector using an angle (like that on a compass) and a magnitude or as two components (i and j).

Later on, in three dimensions you could use i, j, and k components to describe a vector.

In earlier grades, teachers taught cosines and sines only in their relations to triangles, but it turns out that the sine and cosine functions can describe any function (this is related to power series).

Furthermore, a combination of sines and cosines can act as the basis of n-dimensional space.

Thus they prove to be useful far beyond describing triangles.

Tranverse and Longitudinal Waves

From qwerty_gauri on flickr

From qwerty_gauri on flickr

Waves exist in two forms– transverse (like an ocean wave) and longitudinal (like sound waves).

sound wave

sound wave

A transverse wave has a displacement perpendicular to the medium while the displacement of the medium in a longitudinal wave is parallel to the medium.

Thus an ocean wave goes up and down while sound waves compress the air in a parallel way towards the target.

Waves can be periodic, similar to simple harmonic motion, or a single pulse, similar to a pulse moving along a slinky.

And if someone asks you what’s nu, you can say v/lambda.  (physics joke)

Physics of White Water Rafting Bernoulli Pressure

If you go ever go white water rafting you’ll start out in a nice calm area, kind of like the happy singing place on Splash Mountain in Disneyland.

The river is wide at this point and the velocity of the water is fairly low.

Further down the river though the river will narrow and rocks will be there.

According to Bernoulli, p1 + (1/2)ρv12 = p2 + (1/2)ρv22


p is pressure
ρ (rho) is density

and the narrowness will therefore increase the velocity to allow the same amount of water to flow in the same time it takes at the calmer points in the river.

More water has to go through a smaller area so it will need to go faster.

Buoyancy Continued Ice, Salt Water, Pressure

When an object is immersed within a fluid, for example air or water, the volume of the fluid displaced will contribute to an upward force.

The amount of fluid displaced will cause a force of equal magnitude to the weight of that fluid to push upwards.

Ice is about 91.7% the weight of water so therefore 8.3% of a piece of ice would be above water in the case of pure water.

Salt water is a bit more dense and therefore more like 10% of the ice would be above water.

The difference in pressure between the top and bottom of an object makes this movement possible.

Buoyancy and Volume Displacement

Objects that float have something known as buoyancy which is an upward force that exists when the specific object has less density than the surrounding medium.

The mass of the object is important, but the displaced volume is what affects upward force.

Thus a cement canoe can float and a wooden boat can sink- if filled with water– since the effective volume decreases.

Also a ball of clay could be formed into an object with enough volume to float, but Prof. Kesten didn’t quite pull it off in class today while the cap did float- just the other guy and I predicted.

Pressure, equilibrium, and energy conservation

When pressure is exerted it will act and then resolve to equilibrium quickly.

If you squeeze toothpaste it will come out the other end and then stop moving.

Pressure coming from a tire jack can have a very large force, but energy is conserved, so it will be across a small distance.