A 0.55-m-long guitar string emits 220 Hz as its fundamental. The mass of the str

Question

A 0.55-m-long guitar string emits 220 Hz as its fundamental. The mass of the string that is vibrating is 1 gram. What is the period of this oscillation? What is the wavelength of this oscillation? What is the wave speed along the string? What is the linear density Mu of the string? What is the tension in the string? What is the string's second harmonic (2nd Mode or 1st Overtone)? What is the string's third harmonic (3rd mode or 2nd Overtone)? If you pluck the string when your finger is on the 5th fret (so 3/4 of the original length now vibrates), what fundamental frequency is emitted?

Explanation / Answer

(a) Period of Oscillation T = 1/f = 1/220 =0.004545 seconds

(b)Wavelength

We know that lamda = L/2 = 0.55/2 =0.275 m

(c) wave speed

we know that v = f*lamda = 220*0.275 =60.5 m/s

(d) Linear density =mass/length = 1 gm/1000/0.55 =0.001818 kg/m.......Ans.

(e) Tension

we know that v = sqrt(T/mu)

mu= linear density = 0.001818 kg/m

v = 60.5 m/s

T = 60.52*0.001818 =6.655 N

(f) second harmonic =2*f =2*220 = 440 Hz

Third Harmonic = 3*f = 660 Hz

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