Answer :
Final answer:
The frequencies of the first four harmonics for a violin string with a fundamental frequency of 460 Hz are 460 Hz (fundamental), 920 Hz (second harmonic), 1380 Hz (third harmonic), and 1840 Hz (fourth harmonic).
Explanation:
The question is asking about the frequencies of the harmonics for a violin string vibrating at a fundamental frequency of 460 Hz. Based on the principle that harmonics are integer multiples of the fundamental frequency, the first four harmonics can be calculated easily. The second harmonic (first overtone) will be twice the fundamental frequency, the third harmonic (second overtone) three times, and so on.
Using the given fundamental frequency (f1) of 460 Hz:
- First harmonic (fundamental): f1 = 460 Hz
- Second harmonic: f2 = 2 × f1 = 2 × 460 Hz = 920 Hz
- Third harmonic: f3 = 3 × f1 = 3 × 460 Hz = 1380 Hz
- Fourth harmonic: f4 = 4 × f1 = 4 × 460 Hz = 1840 Hz
The frequencies of the first four harmonics for this string are 460 Hz, 920 Hz, 1380 Hz, and 1840 Hz respectively. It is important to note that the tension in the string can affect these frequencies by altering the speed of the waves on the string.
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