Apitch of middle d (first harmonic = 294 hz) is sounded out by a vibrating guitar string. the length of the string is 70.0 cm. calculate the speed of the standing wave in the guitar string. a frequency of the first harmonic is 587 hz (pitch of d5) is sounded out by a vibrating guitar string. the speed of the wave is 600 m/sec. find the length of the string.

f = frequency of first harmonic = 294 Hz

L = length of the string = 70 cm = 0.70 m

wavelength is given as

λ = 2L

inserting the values

λ = 2(0.70)

λ = 1.40 m

speed of standing wave is given as

v = f  λ

v = 294 (1.40)

v = 411.6 m/s

f = frequency of first harmonic = 587 Hz

v = speed of the wave = 600 m/s

L = length of the string

frequency of first harmonic is given as

f = v/(2L)

inserting the values

587 = 600/(2L)

L = 600/(2 x 587)

L = 0.511 m

the independent variable, or the one that is intentionally manipulated is the speed.

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