a guitar string has an overall length of 1.25m and a total mass of 40g (0.04kg)

Question

a guitar string has an overall length of 1.25m and a total mass of 40g (0.04kg) before it is strung on the guitar. Once on the guitar, however, there is a distance of 64cm (0.64cm) between its fixed and end points. It is tightened to a tension of 720 N. a.) what is the mass per unit of the string? b.)what is the wave speed for the waves on the tightened string? c.)what is the wavelength of the traveling waves that interfere to form the fundamental standing wave(nodes just at either end) for this string? d.)what is the frequency of the fundamental wave? e.)what are the wavelength and frequency of the next harmonic (with a node in the middle of the string)?

Explanation / Answer

a)mass per unit length = m/l = 0.04/1.25 = 0.032 kg/m
b)wave speed = (Tl/m)1/2 = (720/0.032)1/2 = 150 m/s

c)given /4 = 0.64 m hence =2.56m

d)freq(fundamental mode)= v/2l = 150/2.5=60

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