A pitch 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