18 The Doppler Effect
199
The third and last point that needs to be fulfilled is that we need an observer with an
instrument, a sensitive tuning fork that oscillates in response to the oscillations of
the medium. For example, if one places a tuning fork on a piano, the fork begins to
oscillate. This is the principle of a resonator. Now every resonator can do more than
oscillate at a single frequency, but the oscillations made at its eigen frequency are
the most strongest. Due to the fact that the observer cannot know the frequency of
the arriving oscillation, he sets up a large number of resonators. The resonator with
its eigen frequency that oscillates the most under the impression of the arriving wave
therefore gives us the frequency of the incoming wave.
We will describe this experiment schematically. The membrane of the standard
emitter oscillates harmonically with a period of oscillation T o , i.e. with frequency
ν o = 1/T o . The observer S sitting on top of the emitter will therefore register that
his membrane strikes the surrounding medium n o times during the time t o ,
ν o =
1
T o
=
n o
t o
.
Frequency of the
emitter S
(224)
This produces a wave of the frequency ˜
ν in the medium. This waves moves through
the medium with the velocity c T ,
˜
ν o .
Frequency of the wave
produced in the medium
(225)
The observer O sitting on the receiver registers an arriving frequency ν , in other
words a harmonic wave with a period of oscillation T , by counting the number n
of wave crests that arrive during the time t ,
ν =
1
T
=
n
t
.
Frequency registered
by observer
(226)
The comparison case that can be seen as a test for the quality of the transmitting
medium will consist in the demand that both emitter and observer are stationary with
respect to the medium. We will also only allow such media to be included, for which
all three frequencies coincide. Taking our considerations from Chap. 4 into mind,
this would apply to the mechanical continuum, which we receive as a limiting case
of the linear chain, see Fig. 18.1,
ν o = ˜
ν = ν.
The static
comparison case
(227)
In all, we will observe three cases.
(I) The emitter moves towards the observer with the velocity v, see Fig. 18.2.
From observer O’s point of view, this would look like the following: The first wave
crest was emitted when the emitter S was located at x o . This wave crest moves with
199
The third and last point that needs to be fulfilled is that we need an observer with an
instrument, a sensitive tuning fork that oscillates in response to the oscillations of
the medium. For example, if one places a tuning fork on a piano, the fork begins to
oscillate. This is the principle of a resonator. Now every resonator can do more than
oscillate at a single frequency, but the oscillations made at its eigen frequency are
the most strongest. Due to the fact that the observer cannot know the frequency of
the arriving oscillation, he sets up a large number of resonators. The resonator with
its eigen frequency that oscillates the most under the impression of the arriving wave
therefore gives us the frequency of the incoming wave.
We will describe this experiment schematically. The membrane of the standard
emitter oscillates harmonically with a period of oscillation T o , i.e. with frequency
ν o = 1/T o . The observer S sitting on top of the emitter will therefore register that
his membrane strikes the surrounding medium n o times during the time t o ,
ν o =
1
T o
=
n o
t o
.
Frequency of the
emitter S
(224)
This produces a wave of the frequency ˜
ν in the medium. This waves moves through
the medium with the velocity c T ,
˜
ν o .
Frequency of the wave
produced in the medium
(225)
The observer O sitting on the receiver registers an arriving frequency ν , in other
words a harmonic wave with a period of oscillation T , by counting the number n
of wave crests that arrive during the time t ,
ν =
1
T
=
n
t
.
Frequency registered
by observer
(226)
The comparison case that can be seen as a test for the quality of the transmitting
medium will consist in the demand that both emitter and observer are stationary with
respect to the medium. We will also only allow such media to be included, for which
all three frequencies coincide. Taking our considerations from Chap. 4 into mind,
this would apply to the mechanical continuum, which we receive as a limiting case
of the linear chain, see Fig. 18.1,
ν o = ˜
ν = ν.
The static
comparison case
(227)
In all, we will observe three cases.
(I) The emitter moves towards the observer with the velocity v, see Fig. 18.2.
From observer O’s point of view, this would look like the following: The first wave
crest was emitted when the emitter S was located at x o . This wave crest moves with