# 6b Midterm 1 Review Sheet

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• Physics 6B Midterm 1 Review Sheet Peter Heuer, January 23rd, 2015

This review sheet is not intended to be all-inclusive, but rather to be guide to the most important concepts and equations.

Oscillations

- A simple harmonic oscillator (SHO) is an object that experiences a force F = kx. The quintessential example is ablock on a spring, although we also model (approximate) lots of other systems as SHOs.

- The position of a SHO satisfies the equation md2xdt2 = kx.

- What are the definitions of period, frequency, and amplitude?

- What is the difference between frequency and angular frequency?

Waves

- Waves are oscillations in some medium, and are often caused by an SHO (like a spring attached to the end of a string).Therefore the shape of a wave can be described using the same vocabulary we developed for SHOs.

- Waves can be either standing waves (like vibrations on a string) or traveling waves (like light or sound waves).

- When two waves meet, their amplitudes ADD (the principle of superposition). If the waves are in sync this causesconstructive interference, increasing the overall amplitude. If the waves are pi out of phase, they interfere deconstructivly,lowering the overall amplitude.

- A string can support standing waves both at its natural frequency and at integer multiples of this frequency, calledharmonics.

Sound

- Sound is a longitudinal wave that travels through air.

- Sound intensity is measured in decibels because of the logarithmic way humans perceive sound: in order to sound twiceas loud, a sound wave must in fact be 10 times more intense.

- When a source of sound is moving towards you, the wavelength is decreased, increasing the frequency. When the sourcemoves away from you, the wavelength is stretched, making the frequency lower. This is called the Doppler Effect.

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• Physics 6B Midterm 1 Review Sheet Peter Heuer, January 23rd, 2015

Not all of these equations are true and/or useful in all situations.While studying, ask yourself when each of these equationsapply!

Constants:

- I0 1012 Wm2 .- c = 3 108ms .

Oscillations

T =1

f

= 2pif

F = kx

md2x

dt2= kx

=

k

m

x = ACos(t+ )

U =1

2kx2

Waves

v = f

D(x, t) = ASin(kx t+ )

vstring =

T

Frequency of standing waves on a string with both endsfixed:

fn = nv

2l

Sound

(in dB) = 10log

(I

I0

)f = (1 +

vobsvsnd

)f

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