Waves

Waves

What is a Wave?

A wave is an oscillation that transmits energy through a medium.

Waves do not transmit matter, only energy.

A pulse is like a wave, but only a single disturbance.

wave medium examples
sound matter (solid, liquid, gas) talking, music
light electro-magnetic fields sunlight, wifi
surface interface between two media ocean waves, ripples
string string whip
traffic cars on a road the 405 @ 5:00pm
seismic solids S and P waves
gravitational spacetime LIGO
electrical wires cable TV, phone lines

Interference

Two waves pass through each other without any effect.

Wave Properties

100m time
amplitude = m           velocity = m/s          wavelength = m
frequency = Hz          period = s

Frequency and period have a mathematical relationship. Let's see if we can build an equation for how they are related.

Use the simulator above to record five different pairs of frequency and period. Graph the pairs with period as the x-coordinate and frequency as the y-coordinate. What does the graph look like?

$$f = \frac{1}{T}$$

\(f\) = frequency [Hz, s⁻¹, hertz]
How often an event happens in a second.

\(T\) = time period [s, seconds]
How many seconds are between each event.

Frequency and period are the inverse of each other. If a wave has a frequency of 2Hz, then 2 wavelengths pass a point in a second, but the period is 1/2s because that is the time for a single wavelength to pass.

Wave on a String
Click to Run

The Wave Equation

$$v = f \lambda \quad \quad v = \frac{\lambda}{T} $$

\(v\) = wave speed [m/s]
\(\lambda\) = wavelength [m, meters]
\(f\) = frequency [Hz, s⁻¹, hertz]
\(T\) = time period [s, seconds]
speed vacuum air water glass
sound (m/s) N/A 340 1,484 4,540
light (m/s) 300,000,000 300,000,000 220,000,000 200,000,000
Example: An air horn sounds at a frequency of 220 Hz. What is the wavelength of the sound wave?
solution

speed of sound at sea level = 340 m/s

$$v = f \lambda$$ $$\lambda = \frac{v}{f}$$ $$\lambda = \frac{340}{220}$$ $$\lambda = 1.54m$$
Example: The distance between successive crests in a series of water waves is 4.0 m, and the crests travel 8.6 m in 5.0 s. Calculate the frequency of a block of wood bobbing up and down on these water waves.
solution
Example: Two students are holding a slinky while standing 3.6 m apart. The first student sends a pulse which travels all the way down and back again. It takes 2.4 s for the wave to return. What is the speed of the wave?
solution

Reflection and Refraction

The Doppler Effect

Diffraction

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