Answer :
The frequencies of the first four harmonics of a violin string vibrating at 266 Hz (fundamental frequency) are: 266 Hz (1st harmonic), 532 Hz (2nd harmonic), 798 Hz (3rd harmonic), and 1064 Hz (4th harmonic).
Harmonics are frequencies that are integer multiples of the fundamental frequency. In the case of a violin string vibrating at 266 Hz as its fundamental frequency, the frequencies of the first four harmonics can be calculated as follows:
1st harmonic: The fundamental frequency itself is considered the 1st harmonic, so it remains at 266 Hz.
2nd harmonic: The frequency of the 2nd harmonic is twice the fundamental frequency. Therefore, the 2nd harmonic frequency is calculated as 2 × 266 Hz = 532 Hz.
3rd harmonic: The frequency of the 3rd harmonic is three times the fundamental frequency. Hence, the 3rd harmonic frequency is 3 × 266 Hz = 798 Hz.
4th harmonic: The frequency of the 4th harmonic is four times the fundamental frequency. Thus, the 4th harmonic frequency is 4 × 266 Hz = 1064 Hz.
In summary, the frequencies of the first four harmonics of the violin string vibrating at a fundamental frequency of 266 Hz are 266 Hz, 532 Hz, 798 Hz, and 1064 Hz.
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