High School

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What is the frequency of pattern Z in the diagram above showing three standing waves that occur on the same string?

The frequency of pattern X is 65.5 Hz and the frequency of pattern Y is 98.3 Hz.

Answer :

Final answer:

The frequency of pattern Z is 196.5 Hz, as it is the third harmonic (second overtone) in the series, with the fundamental frequency given as 65.5 Hz for pattern X.

Explanation:

The frequency of pattern Z in the context of standing waves on a string relates directly to the harmonic series. Given the frequencies for pattern X and pattern Y to be 65.5 Hz and 98.3 Hz, respectively, we can deduce the relationship between these frequencies in terms of harmonics or overtones.

Pattern X is the fundamental frequency (first harmonic), and pattern Y is the second harmonic (first overtone). The frequency of pattern Z, which would be the next harmonic, should be the third harmonic (second overtone). The frequencies of the harmonics are proportional to their mode number, meaning that if pattern X (n=1) is 65.5 Hz, and pattern Y (n=2) is 98.3 Hz, then pattern Z (n=3) would be 65.5 Hz * 3, because it's the third harmonic.

Therefore, the frequency of pattern Z is 196.5 Hz.

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