Unit 9 Notes

Waves

T is Period of oscillation. It is the time it takes to complete one full oscillation.

f is frequency. It is the number of full oscillations that occur in some amount of time (usually 1s).

A is Amplitude. It is the magnitude of the greatest value of the oscillation

𝑻=𝟏𝒇

Pendulums

Because the restorative force is gravity, the acceleration is independent of mass.

𝑻=𝟐𝝅 √ 𝒍𝒈

Oscillating Spring

• Amplitude is the furthest distance from equilibrium.

• Restorative force is the spring force. Divide that by the mass for acceleration.

𝑻=𝟐𝝅 √𝒎𝒌

Side note:• F = -k∆x – in a spring• F = ma

• ma = -k∆x

v = f λ

v is velocity of the wave.

f is frequency of the wave

λ is the wavelength.

Crest: The highest point.Trough: The lowest point.

Wavelength: The distance between corresponding parts of adjacent waves (crest to crest, trough to trough, etc)

-the length of the full wave

Standing Waves

When there are waves traveling both ways through a medium (such as a string), they will interfere with each other.

Node: A point where the waves cancel each other out.

Anti-Node: A point of maximum oscillation half way between nodes.

Reflections

Fixed End: The wave returns on the opposite side (if it was on the left, it’s now on the right. If it was on the top, it’s now on the bottom).

Outgoing: Returning:

Free End: The wave returns on the same side.

Outgoing: Returning:

Changing Media

From heavy to light: Part of the wave reflects. Most of the wave transmits. Both end up on the same side as the original wave.

From Light to Heavy. Part of the wave is reflected and part is transmitted. The reflected part switches sides while the transmitted part stays on the same side.

Interference

When two waves hit each other, they add together. They then pass through each other and continue as if they had never met.

Constructive Interference: When two or more waves add together to create a larger amplitude.

Destructive Interference: When two or more waves cancel each other out.

Constructive Interference

Destructive Interference

Beats-When two waves of different frequencies interact, they interfere with each other

-The beat frequency is the difference between the two original frequencies

The wave pattern to the right shows the interaction between a 293Hz sound wave and a 261Hz sound wave. The combined wave has a beat frequency of about 32Hz. The period is about 0.3s.

Sound in Tubes

An open end of a tube is where you will find an anti-node.

A closed end will be a node.

Modes

The first mode is for the longest wave you can get in the pipe. Each successive mode is for the next longest wave you can fit in the pipe.

1st Mode. λ=4L

2nd Mode. λ=(4L)/3

3rd Mode. λ=(4L/5)

1st Mode. λ=2L

2nd Mode. λ=L

3rd Mode. λ=2L/3