show steps and formulas used please. 3. a guitar string is 40.0 cm long and has

Question

show steps and formulas used please.

3. a guitar string is 40.0 cm long and has been tightened so that the speed of the waves on the string is 800.0 m/s. sketches of the fundamental (first harmonic) and the third harmonic are shown below.

a. what is the wavelength of the fundamental?

b. what is the frequency of the fundamental?

c. what is the wavelength of the sound produced by the string in air?

d. what is the wavelength of the third harmonic?

e. what is the frequency of the third harmonic?

f. what is the wavelength of the sound produced by the string in air?

Explanation / Answer

Part A)

The wavelength is twice the string length

= 2L = (2)(.4) = .8 m

Part B)

v = f

800 = f(.8)

f = 1000 Hz

Part C)

This depends on what your book uses for the speed of sound in air. Mine uses 343, so I will use that

v = f

343 = (1000)

= .343 m   (if your book uses a different value than 343, your answer will be off a little)

Part D)

= 2/3 of the string length

(2/3)(.4) = .267 m

Part E)

v = f

(800) = f(.267)

f = 3000 Hz

Part F)

Again, I will uses 343

343 = (3000)()

= .114 m

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