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Beats

Explore the superposition principle, standing waves, and beats phenomenon in wave theory. Learn how different wave disturbances interact independently, resulting in varying amplitudes over time in a medium. Discover how frequency differences create beats and their impact. Practice calculating average frequencies for comprehensive understanding.

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Beats

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  1. Beats

  2. We have already discussed interference of transverse waves in strings and of water waves in the ripple tank. • There is abundant experimental evidence that two or more wave disturbances can travel through the same medium independently of one another.

  3. The superposition principle shows us that the displacement of a particle of a medium at any time is the vector sum of the displacements it would experience from the individual waves acting alone. A standing wave is formed by two wave trains of the same frequency and amplitude traveling through a medium in opposite directions.

  4. Two wave trains of slightly different frequencies traveling in the same direction through a medium will interfere in a different way. At any fixed point in the medium through which the waves pass, their superposition gives a wave characterized by an amplitude that varies with time.

  5. In curve (A) the frequency is 8 hz, and in (B) it is 10 hz. Curve (C) shows the combined effect of these two waves at a fixed point in their pathway. This resultant wave varies periodically in amplitude with time. Such amplitude pulsations are called beats. • The average human ear can distinguish beats up to a frequency of approximately ten per second.

  6. The number of beats per second equals the difference between the frequencies of the component waves. • To find the average frequency: fav = 1/2(fl + fh)

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