Physics 232. Heat, Sound, and Light

Equations for Exam II - oscillations and waves

Constants, such as values for , bulk moduli, will be provided as needed.

15.1 Force on a mass on a spring

15.6 Equation of motion for mass on a spring

15.9 Angular frequency for mass on a spring

15.10-14 Relations between frequencies and periods.

15.15 Velocity of mass on a spring

15.16 Acceleration of mass on a spring

15.21 Total energy of a simple harmonic oscillator

15.26 Period of a simple pendulum

16-1 Equation for travelling wave
(To right)

(To left)

16.5 Wave function for travelling sinusoidal wave:

where and are the spatial and angular frequency or...                                     y(x,t) = A sin [2*pi(x/lambda - t/T)]
where and are the spatial and temporal periods.

16.12 Golden rule" of waves:

16.14 Transverse speed of sinusoidal wave on string

16.15 Transverse acceleration of sinusoidal wave on string

16.18 Speed of a wave on a string

where is the tension, and is the linear mass density of string 16.- Kinetic energy stored in 1 of a wave on a string

16.20 Total energy stored in 1 of a wave on a string

16.21 Power of sinusoidal wave on string (energy per period T)

17.1 Speed of sound in medium with bulk modulus and density

17.1b Speed of sound in air as a function of temperature

17.2 If the displacement of air elements as sound passes is given by

17.3 then the variation in pressure is given by

17.4 Maximum pressure amplitude for the above wave

17.- Power transmitted by a sound wave through area A

17.5 Intensity of a sinusoidal sound wave

17.- Intensity of a sinusoidal sound wave

17.6 Intensity of a sinusoidal sound wave (in terms of pressure ampl)

17.7 Inverse square law: intensity as function of distance from source

17.8 Sound level in decibels

17.13 Doppler shifted frequency,

where is the frequency at the source, is sound speed, is the observer's speed (negative if away from source), and is the source speed (negative if away from observer).

18.- Superposition principle

18.- Superposition of two sinusoidal waves travelling to the right

where is the amplitude of both waves, is the phase shift between the two waves
18.2 Interference conditions for path length difference
• Constructive:

• Destructive:

• where
18.3 Standing wave - sum of two identical waves travelling in opposite directions