Physics Lab 11 (1)

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Physics 2021 Group: Kaya Brown and Amelia Maughan Lab 11: Beats and Doppler Effect Goals The goal of this lab is to utilize created and identified beats to gain a better understanding of the concepts of wave superposition and interference. Another goal of this lab is to observe frequency shifts and Doppler shifts to find the speed of an object. In this experiment, the speed of objects and sound will be calculated based on changes to frequency. Procedure In Part I, two loudspeakers were connected to Pasco and the frequency and volume of the speakers was manipulated. The beats produced by the speakers were observed and the theoretical beat frequencies were calculated. Two waveforms were set up to visualize the sound being produced by the speakers using the calculated beat frequencies. The superposition was obtained from the resulting purple wave of the two source waves from the speakers. The beat frequencies were adjusted and the change in sound was observed. The waves were traced and the constructive and destructive interferences were labeled. In Part IIa, on a phone, a tone was generated in phyphox and the frequency was observed. A table and graph were constructed showing frequency versus time for the movement of the phone. In Part IIb, the speakers were set to 1000 Hz and the amplitude was increased. On a phone, “Doppler effect” was selected in phyphox. The speaker sound source was turned on and the phone was moved towards and away from the source. A graph was constructed showing the frequency versus time of the Doppler

shifts. A table was constructed showing the peak frequency shifts and calculated speed from the Doppler equation. Error and Precautions A possible source of error could have been excessive background noise while collecting data for the Doppler effect in phyphox. If there was background noise, such as tones from other experiments or talking, this would change the measured frequency and give false data. Another possible source of error could have been not moving the phone quickly enough towards and away from the sound source to properly produce data for the Doppler effect. Results Figure 1.1 Wave Interference with Frequencies Set at F1 = 480 Hz and F2 = 500 Hz f 1 - f 2 = 480 Hz - 500 Hz = -20 Hz

Figure 1.2 Wave Interference with Frequencies Set at F1 = 280 Hz and F2 = 250 Hz f 1 - f 2 = 280 Hz - 250 Hz = 30 Hz Figure 2: Doppler Effect Frequency vs. Time Doppler Shifts f observed = f source ( ? ± ? 𝑜??𝑒??𝑒? ? ± ? ?𝑜???𝑒 )

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= 10 Hz = 1.00 Hz ( 3𝑥10 8 𝑚/? ± 0 3𝑥10 8 𝑚/? ± 1.2 𝑚/? ) Frequency shift: f source - f observer = 10 Hz - 1 Hz = 9 Hz Figure 3: Doppler Effect: Doppler Frequency Shifts Section of graph Frequency value 1 (Hz) Frequency value 2 (Hz) Frequency shift (Hz) 1 999.3 999.61 0.31 2 999.61 1005 5.39 3 1005 995.55 9.45 4 995.55 999.6 4.05 5 999.6 999.53 0.07 Questions Question 1. How could you prove to a skeptic that the beats are an interference effect that requires both sound sources and the phenomenon is not created using a pre-recorded sound? Test out your method to convince yourself. To prove to a skeptic that beats are an interference effect that requires both sound sources and is not created by a pre-recorded sound, you could compare a pre-recorded sound to the sound sources. First, you could play a pre-recorded sound with the sound sources turned off. Then, you could turn on the sound sources which would create a fluctuation in volume, this change is the beats. Question 2. How many times per second should you hear a beat? Does the beat frequency you hear seem to agree with this calculated value?

One beat per second was heard and the beat frequency agrees with this calculation. When F1 was set to 480 and F2 to 500, there were 20 beats per second. Beats per second is equal to the absolute value of frequency of one sound subtracted by the frequency of second sound. Question 3. What magnitude frequency shift did you estimate for moving the phone source? 1 Hz? 10 Hz? 100 Hz? As you move the phone away, do you expect to receive an upward or downward shift in frequency? The magnitude frequency shift used for moving the phone source was 10 Hz. As you move the phone away it will receive a downward shift in the frequency. The 5 regions of the graph are labeled according to the movement instructed in the lab manual. Question 4. Generally speaking, how does the amount of the Doppler frequency shift depend on the magnitude of the source frequency? In other words, at which source frequency 300 Hz or 1000 Hz will the Doppler shift be more noticeable to our ears? Try more observations with other frequencies if you like. The Doppler frequency shift is the difference between the sound heard by the observer and the original sound of the source. The magnitude of doppler frequency shift is more noticeable at 1,000 Hz than at 300 Hz.

Question 5. What are the largest magnitude doppler frequency shifts you see in your data? Use your values for the next step. Highest frequency f 1 = 1004.96 Hz Lowest frequency f 2 = 995.546 Hz Magnitude Doppler frequency shift: f 1 - f 2 = 1004.96 Hz - 995.546 Hz = 9.414 Hz Question 6. What speeds did you find that you moved the phone? Were the values reasonable? (Around a meter per second is typical of the speed of human motion.) The phone was moved at about 1.2 m/s. This is a reasonable speed of human motion and resulted in reasonable values. Discussion The theoretical beat frequency for the two source frequencies at 250 Hz was 1 beat per second. When set F1 was set to 480 and F2 to 500, 20 beats per second was calculated. The waves created by these frequencies reach a peak amplitude where constructive interference is shown and destructive interference occurs at zero amplitude. The frequency shift calculated by the Doppler-shifted frequency and the original source frequency utilizes the equation, f observed = f source . Vobserver was calculated to be zero because the observer is stationary. The (1 ± ? 𝑜??𝑒??𝑒? ? ) largest magnitude doppler frequency shifts found in the data was from 1004.96 Hz to 995.546 Hz, giving a shift of 9.41 Hz.

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