A 52 cm string resonates at the 7th harmonic. What is the wavelength on the string?
First harmonic wavelength (the fundamental) = 104 cm
Second harmonic wavelength = 52 cm
Third harmonic = 104/3 = 34.67 cm
Seventh harmonic = 104/7 = 14.9 cm
Not to be confused with the wavelength of the sound in air.
Some people call the nth harmonic the nth ABOVE the fundamental and do not call the fundamental a harmonic. In that case, your answer would be 104/8 = 13 cm
To find the wavelength on the string, we can use the formula:
λ = 2L/n
where:
λ = wavelength
L = length of the string
n = harmonic number
In this case, the length of the string is 52 cm, and the harmonic number is 7.
Substituting these values into the formula, we have:
λ = 2(52 cm) / 7
Now we can calculate the wavelength:
λ = 104 cm / 7
λ ≈ 14.857 cm
Therefore, the wavelength on the string is approximately 14.857 cm.