A guitar string has a length of 0.650 m and a mass of 4.00 × 103 kg. Part A If i

Question

A guitar string has a length of 0.650 m and a mass of 4.00 × 103 kg.

Part A

If it is kept under a tension of 136 N ,what is the fundamental (smallest harmonic) frequency at which it vibrates?

Express your answer with the appropriate units.

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Part B

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

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A guitar string has a length of 0.650 m and a mass of 4.00 × 103 kg.

Part A

If it is kept under a tension of 136 N ,what is the fundamental (smallest harmonic) frequency at which it vibrates?

Express your answer with the appropriate units.

f1=

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Part B

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

At what other frequencies (higher harmonics) could it vibrate at this fixed length? The string could vibrate at any positive integer multiple of this fundamental frequency nf1. The string could vibrate at frequencies 2f1, 4f1, 8f1, and 16f1. The string could vibrate at frequencies 2f1, 3f1, and 5f1. The string couldn't vibrate at any different frequency.

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Explanation / Answer

Part A)

Use equation,

F= nv/2L

For fundamental frequency n=1

v= sqrt[T/u] = sqrt[ T/(m/L)] = sqrt[136/(0.004/0.65)] = 148.7 m/s

f = (1*148.7)/(2*0.004) = 18587.5 Hz

Part B)

Since can be n=1,2,3,4,5 ..........

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

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