The fundamental frequency of a string instrument is 580 Hz. (i) Calcul

Question

The fundamental frequency of a string instrument is 580 Hz. (i) Calculate the frequency of the first and third harmonics generated on it. (ii) If the tension in the string is doubled, calculate the new fundamental frequency.

23 Apr 2024

Answer :

Word Count : 359

Sure, let's break down this question into parts.

### Part (i): Calculating frequencies of harmonics

The fundamental frequency, denoted as \( f_1 \), of a vibrating string is given as 580 Hz. To find the frequencies of the first and third harmonics:

1. First Harmonic (\( f_1 \)):
The first harmonic is the fundamental frequency itself.
\[ f_1 = 580 \text{ Hz} \]

2. Third Harmonic (\( f_3 \)):
The nth harmonic frequency (\( f_n \)) of a string is given by:
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