Question

A string is fixed at both ends and vibrating at 140 Hz, which is its third harmonic frequency. The linear density of the string is 4.6x10-3 kg/m, and it is under a tension of 2.3 N. Determine the length of the string.

Answer 1

Step-by-step explanation:

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Answer 2

Length of the string = 0.24 m

Step-by-step explanation:

The frequency (f) of vibration of stringed instruments is related to the Tension (T) in the spring by the relation

fₙ = (n/2L)√(T/μ)

where n = 1,2,3,4...

For third harmonic frequency, n = 3

L = length of the string = ?

T = tension in the string = 2.3 N

μ = linear density = 4.6 × 10⁻³ kg/m

f = frequency = 140 Hz

L = (n/2f)√(T/μ)

L = (3/(2×140))√(2.3/0.0046) = 0.40 m