A guitar string has a length of 0.650 m and a mass of 4.00 x 10^-3 kg Part A If

Question

A guitar string has a length of 0.650 m and a mass of 4.00 x 10^-3 kg

Part A

If it is kept under a tension of161N , what is the fundamental (smallest harmonic) frequency at which it vibrates?

Express your answer with the appropriate units.

Part B

At what other frequencies (higher harmonics) could it vibrate at this fixed length?

a] The string could vibrate at any positive integer multiple of this fundamental frequency nf1. b] The string could vibrate at frequencies 2f1, 3f1, and 5f1. c] The string could vibrate at frequencies 2f1, 4f1, 8f1, and 16f1. d] The string couldn't vibrate at any different frequency. A guitar string has a length of 0.650 m and a mass of 4.00 x 10^-3 kg Part A If it is kept under a tension of161N , what is the fundamental (smallest harmonic) frequency at which it vibrates? Express your answer with the appropriate units. f1 = Part B At what other frequencies (higher harmonics) could it vibrate at this fixed length? a] The string could vibrate at any positive integer multiple of this fundamental frequency nf1. b] The string could vibrate at frequencies 2f1, 3f1, and 5f1. c] The string could vibrate at frequencies 2f1, 4f1, 8f1, and 16f1. d] The string couldn't vibrate at any different frequency.

Explanation / Answer

1. fundamental frequency f = (1/2L) sqrt(T/u)

where u = m/l = 4e-3/0.65 = 0.00615

so f = (1/2* 0.65) * sqrt(161/0.00615)

f = 124.42 Hz

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B.a]    The string could vibrate at any positive integer multiple of this fundamental frequency nf1.

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