Two sound waves with f1 = 100 Hz and f2 = 110 Hz are attatched in an image below. They move through air with v = 340 m/s. They superimpose to create the wave f1 + f2. Quantitatively prove or argue against the following: The intensity of f1 + f2 is oscillating with a frequency of 10 Hz. The amplitude of f1 + f2 is oscillating with a frequency of 5 Hz. The inner oscillation frequency of f1 + f2 is 105 Hz.

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Two sound waves with f1 = 100 Hz and f2 = 110 Hz are attatched in an image below. They move through air with v = 340 m/s. They superimpose to create the wave f1 + f2. Quantitatively prove or argue against the following:

  • The intensity of f1 + f2 is oscillating with a frequency of 10 Hz.
  • The amplitude of f1 + f2 is oscillating with a frequency of 5 Hz.
  • The inner oscillation frequency of f1 + f2 is 105 Hz.
The image displays three waveforms that illustrate the concept of wave interference and beats.

1. **Top Waveform (f₁ = 100 Hz):** This is a simple sinusoidal wave with a frequency of 100 Hz. It represents a pure tone at this frequency.

2. **Middle Waveform (f₂ = 110 Hz):** This is another sinusoidal wave, but with a slightly higher frequency of 110 Hz. It also represents a pure tone at this frequency.

3. **Bottom Waveform (f₁ + f₂):** This waveform is the result of adding the two previous waves together. The superposition of these waves creates a phenomenon known as "beats." The waveform shows alternating patterns of constructive and destructive interference, which leads to variations in amplitude. This results in a wave that appears to oscillate in envelope form, where the amplitude periodically increases and decreases.

The differences in frequency (10 Hz) between the two waves lead to these beat patterns, observed in the varying amplitude of this composite waveform. This illustration is a classic example of how interference between two waves of slightly different frequencies can create new wave patterns.
Transcribed Image Text:The image displays three waveforms that illustrate the concept of wave interference and beats. 1. **Top Waveform (f₁ = 100 Hz):** This is a simple sinusoidal wave with a frequency of 100 Hz. It represents a pure tone at this frequency. 2. **Middle Waveform (f₂ = 110 Hz):** This is another sinusoidal wave, but with a slightly higher frequency of 110 Hz. It also represents a pure tone at this frequency. 3. **Bottom Waveform (f₁ + f₂):** This waveform is the result of adding the two previous waves together. The superposition of these waves creates a phenomenon known as "beats." The waveform shows alternating patterns of constructive and destructive interference, which leads to variations in amplitude. This results in a wave that appears to oscillate in envelope form, where the amplitude periodically increases and decreases. The differences in frequency (10 Hz) between the two waves lead to these beat patterns, observed in the varying amplitude of this composite waveform. This illustration is a classic example of how interference between two waves of slightly different frequencies can create new wave patterns.
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