# Worksheet: Beat Frequencies

In this worksheet, we will practice relating the beat frequency produced by the superposition of two waves to the waves' frequencies.

**Q1: **

What beat frequency is produced by two sound waves that have frequencies of 102 Hz and 97 Hz? Answer to one significant figure.

**Q2: **

Two sound waves produce a beat frequency of 2.4 Hz. The higher-frequency sound wave has a frequency of 1,025.8 Hz. What is the frequency of the other sound wave? Answer to five significant figures.

**Q3: **

When two waves that have slightly different frequencies are superposed, they produce a beat frequency. Which of the following formulas correctly relates the frequencies of the two waves, and , where , to the beat frequency, ?

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**Q4: **

The diagram shows two traveling waves, shown in orange and in blue, and the resultant wave of the superposition of the two waves, shown in black. The envelope of the beat frequency produced by the two traveling waves is shown by the dashed gray line.

What is the ratio of the frequency of the wave shown in orange to the frequency of the wave shown in blue?

What is the ratio of the frequency of the wave shown in blue to the frequency of the envelope of the beats produced?

The waves in the diagram are plotted on a grid consisting of equal-length squares. What is the difference between the number of wavelengths per square of the waves shown in orange and the waves shown in blue?

**Q5: **

The four graphs shown represent the envelopes of the beat frequencies generated by four different pairs of sound waves. The part of the time axis containing the envelope on each graph represents the same time interval.

Which envelope is produced by the pair of sound waves with the greatest difference in frequency from each other?

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Which envelope is produced by the pair of sound waves with the least difference in frequency from each other?

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**Q6: **

A sound wave has a frequency of 4,515 Hz. Another sound wave has a frequency slightly lower than the first sound wave. The two sound waves produce a beat frequency that is just at the threshold of human hearing, which is 20 Hz. What is the ratio of the frequency of the higher-frequency sound wave to the frequency of the lower-frequency sound wave? Answer to four significant figures.

**Q7: **

The graph shows the displacement against time of the resultant wave of the superposition of two waves with different frequencies. It displays a beat frequency.

What is the frequency of the beats produced by the superposition of the waves?

The wave that has the greater frequency has a frequency of 2.5 kHz. What is the frequency of the other wave?

**Q8: **

A wave with amplitude 1.0 cm and frequency is initially in phase with another wave with the same amplitude and frequency . Graph I shows the change of displacement with time of the wave with frequency . Graph II shows the wave resulting from the superposition of the waves. The envelope of the beat frequency produced by the waves modulates the amplitude of the resultant wave.

Which of the following graphs correctly shows the wave that has the frequency ?

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**Q9: **

Two waves with similar frequencies are shown in the graph. What is the beat frequency that the waves produce? Give your answer to one significant figure.

**Q10: **

A wave with an amplitude of 1.0 cm and a frequency of is initially in phase with another wave with the same amplitude and a frequency of . Graph I shows the change of displacement with time of the wave with frequency . Graph II shows the change of displacement with time of the wave with frequency .

Which of the following graphs correctly shows the resultant wave of the superposition of the two waves?

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