The sixth harmonic of a 70 cm long guitar string has a frequency of 557.14 Hz. What is the velocity of sound in the guitar string?
Using fn = (nv)/(2L) and plugging in values as fn = f6 = 557.14 = (6v)/(2*0.7) and solving for v, we get v = 130 m/s.
To find the velocity of sound in the guitar string, we need to use the formula:
velocity (v) = frequency (f) × wavelength (λ)
In this case, we are given the frequency of the sixth harmonic (f = 557.14 Hz) and the length of the guitar string (L = 70 cm).
To calculate the wavelength, we need to determine the length of a single wave, which corresponds to the sixth harmonic.
The length of the guitar string (L) is half of the wavelength of the fundamental frequency. So, the wavelength (λ) for the fundamental frequency (first harmonic) can be calculated as:
λ₀ = 2 × L
Therefore, λ₀ = 2 × 70 cm = 140 cm
Since the given frequency is for the sixth harmonic, the wavelength for the sixth harmonic can be calculated as:
λ₆ = λ₀ ÷ 6
So, λ₆ = 140 cm ÷ 6 = 23.33 cm
Now, we can substitute the values into the formula to find the velocity of sound:
v = f × λ₆ = 557.14 Hz × 23.33 cm = 12981.24 cm/s
The velocity of sound in the guitar string is approximately 12981 cm/s.