Peoples Physics Book Version-2

12.3. Key Equations http://www.ck12.org

12.3 Key Equations

Basics

T=

1

f

[1] Wave period

v=λf [2] Wave velocity

Common Frequencies

fbeat=|f 1 −f 2 | [3] Beat frequency from waves of frequencyf 1 andf 2

fn=

nv

2 L

|integern [ 4 ]Standing waves restricted or unrestricted at both ends

fn=

nv

4 L

|odd integern [ 5 ]Standing waves restricted at one end

The Doppler Effect

When a source of a wave is moving towards you, the apparent frequency of the wave you detect is higher than that
emitted. For instance, if an ambulance approaches you while blaring a siren at 500 Hz, the sound you hear will be
slightly higher. This familiar phenomenon is known as theDoppler Effect.The opposite occurs for when the source
is moving away. If the observer is moving also, it is the relative velocities that matter. There is a difference in the
quantitative effect, depending on who is moving. (See the formulas below.) Note that these equations are for sound
waves only. While the effect is similar for light and electromagnetic waves the formulas are not exactly the same as
for sound.

Doppler Shifts:

fo=f

v+vo

v−vs

fo(observed frequency)is shifted up when source and observer moving closer

fo=f

v−vo

v+vs

fo(observed frequency)is shifted down when source and observer moving apart,where

vis the speed of sound,vsis the speed of the source, andvois the speed of the observer