To produce beats , the generating waves must have

Options

A. different frequencies
B. slightly different frequencies
C. slightly different frequencies and same amplitude
D. slightly different frequencies and different amplitude

Answer

To produce beats, the generating waves must have different frequencies. Here's the step-by-step explanation:

1. **Understanding Beats**: Beats are a phenomenon that occurs when two sound waves of slightly different frequencies interfere with each other. This interference results in a variation in sound intensity, which we perceive as alternating loud and soft sounds.

2. **Conditions for Beat Production**: For beats to be produced, the two sound waves must have different frequencies. Let's denote these frequencies as \( f_1 \) and \( f_2 \).

3. **Frequency Difference**: The difference between these two frequencies is crucial. If the frequencies are too close together, the beats will be produced, but if they are too far apart, the sound will not exhibit the characteristic beat pattern. The difference in frequency can be expressed as \( |f_1 - f_2| \).

4. **Persistence of Hearing**: If the difference in frequencies is not significant enough, our ear may not be able to distinguish between the two frequencies due to the persistence of hearing. This means that the ear retains the perception of a sound for a short period after the sound has stopped.

5. **Conclusion**: Therefore, to produce audible beats, the generating waves must have different frequencies, and the difference should be within a range that allows our auditory system to perceive the alternating loud and soft sounds.