The Mystery Frequency: Solving the Beat Phenomenon

Determining the Unknown Frequency

When two frequencies are played simultaneously, a beat with a specific frequency is heard. In this case, the first student is using a frequency generator set to 440 Hz, while the second student has an identical generator playing an unknown frequency. The beat frequency heard is 2 Hz.

The formula to calculate the beat frequency is:

b = |f₁ - f₂|

Where:

b = beat frequency

f₁ = frequency of the first sound

f₂ = frequency of the second sound

Given that:

f₁ = 440 Hz

b = 2 Hz

Using the formula, we can solve for the unknown frequency (f₂):

440 - f₂ = 2 or 440 - f₂ = -2

f₂ = 438 Hz or 442 Hz

Therefore, the unknown frequency that the second student is playing is either 438 Hz or 442 Hz. By analyzing the beat phenomenon, we can accurately determine the frequency of the second sound based on the difference in frequencies.

Understanding the beat phenomenon and its relationship to frequency is essential in audio analysis and music production. By applying the principles of wave interference, we can solve for unknown frequencies and create harmonious compositions.

Next time you hear a beat between two sounds, remember that it's not just a coincidence – it's a result of the fascinating interaction of frequencies!