What are the first three harmonics of a note produced on a 0.31 m long violin string if the waves on this string have a speed of 274.4 m/s
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To determine the first three harmonics of a note produced on a violin string, we need to use the formula for the fundamental frequency:
fundamental frequency (f) = speed (v) / wavelength (λ)
The fundamental frequency is the frequency of the lowest and loudest vibration mode of the string. The harmonics are integer multiples of the fundamental frequency.
First, let's find the wavelength of the fundamental frequency. Given the speed of the waves on the string (v = 274.4 m/s) and the length of the string (L = 0.31 m), we can use the formula:
λ = 2L
λ = 2(0.31 m) = 0.62 m
Now, let's find the fundamental frequency (first harmonic):
f₁ = v / λ
f₁ = 274.4 m/s / 0.62 m = 442.58 Hz
The first harmonic has a frequency of 442.58 Hz.
To find the second harmonic, we need to multiply the fundamental frequency by 2:
f₂ = 2 * f₁
f₂ = 2 * 442.58 Hz = 885.16 Hz
The second harmonic has a frequency of 885.16 Hz.
Similarly, to find the third harmonic, we multiply the fundamental frequency by 3:
f₃ = 3 * f₁
f₃ = 3 * 442.58 Hz = 1327.74 Hz
The third harmonic has a frequency of 1327.74 Hz.
Therefore, the first three harmonics of a note produced on a 0.31 m long violin string with a wave speed of 274.4 m/s are:
1st harmonic: 442.58 Hz
2nd harmonic: 885.16 Hz
3rd harmonic: 1327.74 Hz