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Beat patterns in sound waves - results

Figure 2 shows a typical trace of the sound wave beating.

Screenshot of output waveform

Figure 2: shows the captured screen shot of the beat waveform.

Answers to questions

Q1. Estimate the beat frequency of the sound wave.
A1. Frequency is calculated using the frequency formula:

Frequency = (time taken for one complete cycle to pass)-1

From the graph we measured that a beat occurs every 40 ms.

Beat frequency = (40 ms)-1 = 25 Hz

Q2. Estimate the frequencies of the two sound waves from the signal generators. 
A2. From the graph we measured 1 cycle in 2233 ms.

Frequency of the combined signal = (2233 ms)-1 = 448 Hz

The two frequencies can now be calculated using the combined frequency and the beat frequency. Frequencies of the initial waveform = Frequency of the combined waveform ± the beat frequency.

Frequency of initial sound waves = 448 Hz ± 25 Hz
f1= 423 Hz and f2= 473 Hz

The two frequencies were measured to be 423 Hz and 473 Hz using the frequency meter in PicoScope, this gave a beat frequency of 24 Hz (this should be 25 Hz, the error was probably due to the setting of the signal generators). Figure 3 below shows the output from the spectrum analyzer.

spectrum of sound waves

Figure 3: shows the spectrum of the sound waves.

Q3. What would happen if the amplitudes of the two sound sources were not equal?
A3. If the two sound waves are at similar frequencies but of different amplitudes the two sound waves would not cancel each other out at the destructive interference points. This sound wave would look like the one shown in figure 4.

screenshot of different amplitude waveforms

Figure 4: shows the captured screen shot of the beat waveform with frequencies of different amplitudes.

Figure 5 show the spectrum of the combined waveforms, showing the difference in magnitude of the two wave forms.

screenshot of different amplitude waveform

Figure 5: shows the spectrum of the beat waveform with different amplitudes.

Credits, comments and further info

This experiment was written by Dick Robinson of Maesydderwen School.