Doppler effect (Item No.: P )

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Valentine Gilmore
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1 Teacher's/Lecturer's Sheet Doppler effect (Item No.: P ) Curricular Relevance Area of Expertise: Physik Education Level: Klasse Topic: Akustik Subtopic: Schwingungen und Wellen Experiment: Doppler - Effekt Difficulty Preparation Time Execution Time Recommended Group Size Easy 10 Minutes 10 Minutes 1 Student Additional Requirements: Experiment Variations: Microphone PC Keywords: Task and equipment Information for teachers Additional information In the preliminary experiment, the Doppler effect as it is known from everyday life is recalled to the students mind in a qualitative manner based on an audible frequency, while the main experiment focuses on the case of a harmonically oscillating sound source. First, the frequency of the emitted signal is measured at rest. Then, the frequency shift that is caused by the oscillating Doppler transmitter is proved with the aid of the software. This is followed by the calculation of the velocity of movement of the sound source based on the experimental values. This calculated value is then compared to the theoretical value. This method is particularly elegant since it is a contactless velocity determination procedure that does not require any knowledge concerning the frequency of the emitted signal. In medical applications, for example, the Doppler effect is used to determine the blood stream velocity by way of ultrasound externally through the tissue of the patients. Notes concerning the execution of the experiments Part 1: Frequency shift in the audible range via a quick movement of the Doppler transmitter The effect can be observed better if the experiment is performed by two persons. Part 2: Determination of the frequency shift of the signal with the aid of the software The high frequency of the Doppler transmitter of 19 khz has been selected because - it ensures that the maximum frequency resolution can be achieved, - this pitch is not audible and, therefore, not irritating for humans, and - it can still be processed reliably by standard sound adapters. The frequency of the Doppler source is electronically stabilized to be constant. If you observe a noticeable descent of the frequency (more than 10 Hz in 3 minutes), this is due to a low voltage level (less than 6 V). Please change the battery of the Doppler source. The frequency of the Doppler source lies in a range of 19 khz ±10 % (deviation occurs because of tolerances in the electronic components). The indicated values in the measurement table are therefore to be regarded as examples. Notes concerning the execution of the experiment The experiment should be performed by two students. Derivation of the formula (moving sound source, observer at rest)

2 Teacher's/Lecturer's Sheet distance between the sound source and the observer at the beginning duration of an oscillation Now, the following 4 points of time are taken into consideration: The sound source starts to emit the first wave crest. The observer perceives wave number 1. The sound transmitter starts to emit the second wave crest. In the mean time, the sound transmitter has continued to move and has travelled the distance. As a result, the distance between the transmitter and receiver has been reduced to. The observer perceives wave number 2. This means that the observer perceives a wave with the period. If the time interval between two successive waves is, this corresponds to a frequency observers as well as the formula when both move can be derived.. Correspondingly, the formula for sound sources at rest and moving Derivation of the formula The frequency of the sound of the vehicle is when it approaches the observer, and it is when it recedes from the observer. A division of the two fractions leads to In the right-hand part of the last line, only the interval needs to be known in order to determine the velocity. The frequencies themselves are not required. The two tones of a fifth. for example, have the ratio 4:3, regardless of the frequencies of the emitted (original) signal. This, in turn, leads to the velocity

3 Doppler effect (Item No.: P ) Task and equipment Task When an ambulance passes by, the percei-ed (measured) signal of the siren becomes deeper. This means that the frequencies of the percei-ed sound become lower. This change in the percei-ed frequency of wa-es of all kinds, while the source and obser-er mo-e relati-e to each other, is called the Doppler effect. The Doppler effect is used in numerous technical applications, such as in traffic radar traps or for determining the speed at which the uni-erse is expanding. 1. When the Doppler transmitter emits a sound of 4.6 khz, mo-e it -ery quickly to and fro and describe what you hear. 2. Determine the -elocity of an oscillating spring pendulum with the aid of the Doppler effect: Let the Doppler transmitter with the 19 khz signal oscillate harmonically abo-e a microphone with the aid of a spring. Analyse the signal that was recorded by a microphone with the aid of a computer. Obser-e the Doppler effect and determine the maximum -elocity of the pendulum. Equipment Position No. Material Order No. Quantity 1 Software "Measure Acoustics", single user license Doppler source for TESS Acoustics Helical spring, 3 N/m Measuring tape, l = 2 m Additional material Set-up and procedure Microphone 1

4 Part 1: Frequency shift in the audible range via a quick movement of the Doppler transmitter Select a frequency of 4.6 khz. Mo-e the Doppler transmitter repeatedly and quickly towards and away from your ear or face (or the ear or face of your classmate). Note down how you percei-e the frequency of the signal in the report under "Result - Obser-ations 1". Part 2: Determination of the frequency shift of the 19 khz signal with the aid of the software Connect the microphone correctly to the computer. Open the audio settings of the PC. Set the recording sound -olume of the microphone to maximum. Start the software "measure Acoustics". Open the experiment "3.7a Doppler effect". Help 1: Open the experiment o-er-iew (Menu "File" "Open experiment" or select "Open experiment" on the menu bar. Open the folder "3 Applications in the field of medicine, music and e-eryday life" and select the experiment "3.7a Doppler effect, alternati-e 1". Select a frequency of 19 khz at the Doppler transmitter and switch it on. Note down the approximate -alues of the maximum of the frequency of the transmitted signal in the report under "Result - Obser-ations 2". Help 2: Select the magnifying glass "Zoom" in the corresponding diagram window. Press and hold the mouse button and drag a rectangle from the upper left-hand corner to the lower right-hand corner. Help 3: Use the crosshair "Mark" on the grey bar in the diagram window in order to determine the x--alue (here: frequency in Hz) and the y--alue (here: relati-e amplitude of the sound pressure in %) at the location of the crosshair. Read the two -alues off the status bar at the bottom of the screen (Fig. 3).

The inter-al should co-er a range of about 1000-2000 Hz around the maximum of the frequency of the transmitted signal.

5 Fig. 2: Frequency analysis The frequency of the transmitted signal can also be read off the "Frequency analysis" window (freq = Hz) (Fig. 2) Now set the frequency range for the measurement in the "Frequency analysis" window (Fig. 2). The inter-al should co-er a range of about Hz around the maximum of the frequency of the transmitted signal. (Example: The measurement of the maximum of the frequency of the signal resulted in app Hz. Set the minimum frequency -alue to Hz and the maximum frequency -alue to Hz.) Perform the experiment as shown in Fig. 1. Fig. 3: Frequency spectrum of the recei-ed signal Student 1: Hold the spring on one end and attach the Doppler transmitter to the other end. The spring extends to a rest position. Place the microphone on the floor directly below the Doppler transmitter. Align the microphone upwards towards the transmitter. Student 2: Hold the measuring tape so that it approximately forms an extension of the spring. The zero of the scale must be located at the lower end of the Doppler transmitter. The measuring tape and the spring are slightly offset so that the Doppler transmitter can be deflected without touching the measuring tape. Acti-ate the frequency analysis by selecting "start". Student 2: Pull the Doppler transmitter 20 cm down towards the floor or microphone and release it. Describe what the cur-e in the diagram window "Spectrum of the signal at the audio input (microphone)" looks like and how it has changed after se-eral oscillations in the report under "Result - Obser-ations 3". Stop the measurement of the frequency after some oscillations by selecting "stop". Note down the highest (f max ) and the lowest (f min ) frequency -alue towards which the maximum of the cur-e shifts in the report under "Result - Table 1". Obser-e and note down how the maximum and minimum are connected to the deflection of the spring in the report under "Result - Obser-ations 4". Repeat these measurements se-eral times.

7 Report: Doppler effect Result - Observations 1 (10 Punkte) Part 1: Frequency shift in the audible range via a quick movement of the Doppler transmitter Describe how you perceive the sound during the movement of the transmitter. Result - Observations 2 (10 Punkte) Part 2: Determination of the frequency shift of the signal with the aid of the software Frequency of the transmitted signal at rest: f 0

8 Result - Observations 3 (10 Punkte) Describe how the greatest (smallest) value of the frequency f max (f min ) towards which the maximum shifts changes after several oscillations. Result - Table 1 (24 Punkte) Note down the greatest/smallest value of the frequency towards which the maximum of the curve shifts after only a few oscillations. f min in Hz f max in Hz f max - f min in Hz f max + f min in Hz Measurement 1 19, , ,528 1 Measurement 2 19, , ,523 1 Measurement 3 19, , ,518 1 Measurement 4 19, , ,518 1 Measurement 5 19, , ,519 1 Mean value 19, , ,521 1

9 Result - Observation 4 (10 Punkte) Describe how f max and f min are connected to the deflection of the spring. What is the deflection at which the frequency f 0 is received? Evaluation - Question 1 (10 Punkte) Explain how the change of the curve over time is connected to the deflection and velocity of the spring pendulum.

10 Evaluation - Question 2 (10 Punkte) Use the formula and the measured values of and in order to calculate the maximum velocity of the spring pendulum (c = 343 m/s). Use the mean values of and. When does the spring pendulum reach this velocity? Evaluation - Question 3 (10 Punkte) Calculate the theoretically greatest values of the velocity. at which the spring pendulum moves (spring constant D = 3 N/m, mass m = 0.11 kg). Compare the result to the value that was determined experimentally in 2.

11 Evaluation - Question 4 (10 Punkte).ased on the formula, explain why the Doppler effect can only be perceived at high frequencies or speed of the sound source.

12 Evaluation - Question 5 (10 Punkte) The Doppler effect can be used to calculate the speed of a passing car in a purely acoustic manner. This method works for the siren of an ambulance as well as for the sound of the engine of a car. The frequency of the rest signal is not required for this purpose. Example: The maximum within the frequency spectrum of a passing race car shifts from approximately f 1 = 960 Hz to approximately f 2 = 640 Hz. Calculate the speed at which the race car passes by the spectators stands. Note: With a bit of training, musical people can determine the intervals solely based on their sense of hearing. The formula that is stated above (rearranged so that only fractions of the type are included) can be used to estimate velocities rather precisely without any technical aids and without knowledge of the frequencies. The following table shows some intervals together with the associated velocities.

Determination of an unknown frequency (beats)

Teacher's/Lecturer's Sheet Determination of an unknown frequency (beats) (Item No.: P6011900) Curricular Relevance Area of Expertise: Physics Education Level: Age 16-19 Topic: Acoustics Subtopic: Wave