免费弦振动计算器
计算振动弦的基频和谐波频率。
频率
207.83 Hz
Frequency vs Harmonic Number (n)
公式
## Vibrating String A string fixed at both ends supports standing waves whose frequencies depend on string length, tension, and mass per unit length. ### Formula **f_n = (n / 2L) * sqrt(T / mu)** where T is tension, mu is linear mass density (kg/m), L is string length, and n is the harmonic number.
计算示例
A guitar string: L = 0.65 m, T = 73 N, mu = 0.001 kg/m, fundamental.
- 01v = sqrt(T / mu) = sqrt(73 / 0.001) = sqrt(73000) = 270.2 m/s
- 02f = (1 / (2 * 0.65)) * 270.2
- 03f = 0.769 * 270.2
- 04f = 207.8 Hz
常见问题
How does tightening a guitar string change the pitch?
Increasing tension increases the wave speed on the string, which raises the frequency and thus the pitch.
Why do thicker strings produce lower notes?
Thicker strings have greater linear density (mu), which reduces wave speed and lowers the frequency.
What are harmonics on a string?
Harmonics are integer multiples of the fundamental frequency. The second harmonic is twice the fundamental, the third is three times, and so on.
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