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Wave interference happens when two or more waves meet while traveling through the same medium. It’s like when you throw two stones into a pond and see the ripples collide.

This interaction can either reinforce the wave, making it bigger, or cancel part of it out, making it smaller.

• **Constructive interference** occurs if the waves align perfectly, leading to amplification, such as louder sounds in acoustics.
• **Destructive interference** happens when the waves do not align, canceling each other out partially or completely, leading to softer sounds.

This principle is what causes beats when sound waves of slightly different frequencies interfere. You’ll hear the sound getting louder and softer at regular intervals, which is the beat frequency.

The frequency difference is the key to understanding beats. When two sound waves with slightly different frequencies interfere, they create a third wave with a frequency that is the difference between the two original frequencies.

To understand this better, picture two waves occurring slightly out of sync:

• **Beat frequency** is simply the absolute value of the difference between these two frequencies.
• For example, if you hear 3 beats per second, the frequency difference is 3 Hz.

In the given problem, the original frequency is 200 Hz, and the beat frequency is 3 Hz. So, the frequencies differ by 3 Hz, leading to the new frequency being either 197 Hz or 203 Hz. Since one string was tightened, resulting in a higher frequency, the answer is 203 Hz.

Musical acoustics is the science of sound as it relates to music. In musical acoustics, understanding how different frequencies interact is crucial.

Here, the concepts of beats and frequency differences directly apply. When two notes are played together, their frequencies can create beats, giving rise to harmonious or dissonant sounds depending on the frequencies' ratios.

• **Harmony** results when frequencies are integer multiples or small whole number ratios.
• **Dissonance** occurs with awkward ratios, frequently producing noticeable beats.

Musicians and instrument tuners use this principle to ensure that instruments are in tune. By listening to the rate and intensity of beats produced by interacting sound waves, they can finely tune their instruments. In the given problem, the resulting 3 Hz beat indicates a subtle but perceptible tension change in the string.