Some effects that change wave properties: Propagation in
non-uniform medium
Simple waves propagate in the medium that have fixed
speed of the waves v and thus have specific
frequency f and wavelength λ
related by f λ =v
What happens if the properties of the meidum are not uniform,
for example temperature of the gas or density of the metal rod changes ?
speed of the wave have to change
relation f λ =v still holds ( it is local )
Something, frequency or wavelength, or both have to change.
Frequency does not change - if you push a piece of gas with
a particular frequency, it reacts with the same frequency, and pushes at the
next piece with the same frequency
So what changes is the wavelength
Indeed, if v decreases,
in the same time interval (equal say the period)
the perturbations propagates over a shorter distance, creating shorter
wave.
Of course, if the properties of the materials change too rapidly, part
or all of the wave will reflect of such "boundary"
Doppler effect as frequency changing effect
Doppler effect arise when receiver and/or emitter of a wave
move relative to each other.
Motion of the receiver (listener)
In case of sound the wave propagates in the medium that we condider at rest
If the receiver (listener) moves wrt to the air,
the frequecy of the sound that it receives is
fL = (v + vL )/ λ = f (v+vL)/v
The frequency and wave length of the wave in the air is the reference
f and λ.
Important is the sign of the effect We consider vL
positive if receiver moves towards the source . Then the
frequency at the receiver is higher than the frequency of the wave.
Motion of the emitter (source)
If the source moves wrt to the air, its oscillations at frequency
fS produce the wave in the medium with wavelength
not v/fS but
λfront = ( v - vS ) / fS
in fron of the source and
λbehind = ( v + vS ) / fS
behind the source.
The wave still has speed v so behind the source
its frequency adjusts to be
f= v/λbehind = fS v / (v+vS)
This frequency is the freuency of the wave that a listener behind
the source will receive. If listener does not move wrt air, it will be
the frequency it hears.
Important is the sign of the effect We consider vS
positive if the source moves away from the receiver. Then the
frequency of the wave lower than the frequency of the source.
Combinining two results when both the source and receiver moves
wrt the air, we obtain (speed of sound is positive, speed of receiver
and the source is positive in the direction from the receiver
to the source)
fL = f (v+vL)/v = fS (v+vL)/(v+vS)
Doppler effect when reciever and the source move not strictly towards
each other
When the source and or receiver move strictly towards each other
with constant velocity, the Doppler frequency shift does not depend
on the distance between them.
So as the source apporoaches, frequency at the receiver is higher, when
source passes the listener, frequency abruply drops to lower.
If the move tangentially, it is only component of velocity
towards each other that matters, and that changes with time.
So as the source approaches and then recedes, frequency that we hear
changes continously from higher that was emitted to lower than was emitted
by the source.