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An unfingered guitar string is 0.68 m long and is tuned to play E above middle C (330 Hz).

a) How far from the end of this string must a fret (and your finger) be placed to play A above middle C (440 Hz)?
b) What is the wavelength on the string of this 440-Hz wave?
c) What are the frequency and wavelength of the sound wave produced in air at 22°C by this fingered string?

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Answer:

Length (L2) = 0.51m

Wavelength of string (∆) = 1.02m

Wavelength of sound produced = 0.7795m

Explanation:

Using the equation L1F1 = L2F2

L1 = 0.68m, F1 = 330Hz, F2 = 440Hz

Therefore, (0.68m)(330Hz) = (L2)(440Hz)

L2 = 0.68m × 330hz/440hz

L2 = 0.51m

0.68m - 0.51m = 0.17m from the but

B. ∆ = 2×length (L2)

∆ = 2(0.51) = 1.02m

C. Frequency (f) = 440Hz

V = ∆f

343m/s =∆×440hz

∆ = 343m/s/440hz

∆ = 0.7795m

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