LABORATORY EXERCISE #4
THE DOPPLER EFFECT, BEATS AND THE SPEED OF SOUND
I. INTRODUCTION
Consider a wave emitted by a source that moves at constant velocity which is detected by a receiver which
is also moving at constant velocity. The relationship between the detected and emitted frequencies is
= ( ) (1)
where v is the speed of sound, f is the frequency detected by the detector moving with velocity vo and f is
the frequency emitted by the emitter (as measured when it is motionless) moving with velocity vs. The sign
in the numerator indicates whether the detector is moving towards the source, positive, or away from it,
negative, regardless of whether the source is moving and in which direction it is moving. Similarly, the
sign in the denominator indicates whether the source is moving towards the detector, negative, or away from
it, positive, again regardless of whether the detector is moving and in which direction it is moving. This
equation defines the Doppler Effect, see section 16-7 Giancoli 4th Ed.
When waves of two different frequencies reach a detector, the detected wave will be the sum of each of the
individual waves based on the Superposition Principle. The detected wave will have a frequency which is the
average of the two frequencies and the amplitudes of this wave will be modulated by an envelope whose
frequency will be the difference between the two detected frequencies. This latter frequency is called the beat
frequency (see section 17-8 of your textbook).
Consider a source which emits a wave of frequency f travelling at a speed vs towards a stationary detector.
The wave which reaches the detector will have a frequency f. The difference between f and f can detected
and this will be the beat frequency. Therefore, if the speed of the emitter and the beat frequency are known
then the speed of sound can be determined using the equation for the Doppler Effect.
II. THE EXPERIMENT
The experimental setup consists of two transducers, a photogate and a glider moving on a frictionless air
track. One transducer, the emitter, is mounted on the glider which is equipped with a trigger flag (a piece of
metal of width L) which, in turn, will trigger the photogate. The glider on the air track is used to carry the
moving source. A second transducer, the receiver, is stationary and it is placed at one end of the air track.
Both transducers operate in the ultrasonic range, approximately 40 kHz.
The signals from the moving source and the stationary receiver are sent to one oscilloscope where they are
electronically subtracted. Since the frequencies are slightly different, the resulting signal contains beats. This
beat frequency can also be measured using the oscilloscope.
The trigger flag on the glider interrupts the signal from the photogate and the interval of time that the signal
is blocked can be obtained using the second oscilloscope. Hence, the velocity of the cart can be determined.
Note that the flag triggers both oscilloscopes.
MEASUREMENTS AND CALCULATIONS
Record the frequency emitted by the stationary transducer (use the value given by the oscilloscope).
Press the run/stop button on both oscilloscopes.
GENTLY push the glider away from the detector.
Both oscilloscopes will start acquiring data when the flag blocks the photogates.
One oscilloscope will give the time the flag took to cross the photogates. Using the cursers, measure
this time and calculate the speed of the glider.
The second oscilloscope will display a superposition of the emitted and detected frequencies by the
LABORATORY EXERCISE #4: THE DOPPLER EFFECT, BEATS AND THE SPEED OF SOUND PAGE 1 OF 3
transducers. Using the cursers, measure the beat frequency.
Repeat for several speeds.
Express the speed of the glider as a function of beat frequency and determine the speed of sound
using the best method.
III. LAB REPORT
The instructor will give you details about the lab report.
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