A guitar string with mass density = 2.2 × 10 -4 kg/m is L = 1.05 m long on the g

Question

A guitar string with mass density = 2.2 × 10-4 kg/m is L = 1.05 m long on the guitar. The string is tuned by adjusting the tension to T = 105.7 N.

1)

With what speed do waves on the string travel?  

m/s

2)

What is the fundamental frequency for this string?  

Hz

3)

Someone places a finger a distance 0.166 m from the top end of the guitar.

What is the fundamental frequency in this case?  

Hz

4)

To “down tune” the guitar (so everything plays at a lower frequency) how should the tension be adjusted?

increase the tension

decrease the tension

changing the tension will only alter the velocity not the frequency

Explanation / Answer

1) v = sqrt(T/mu) = sqrt(105.7/(2.2*10^-4)) = 693.14 m/sec

2) funamental frequency is f1 = v/(2*L) = 693.14/(2*1.05) = 330 Hz

3) no.of loops formed was 1.05/0.166 = 6 loops

Now funmental frequency is f = v/(2*L) = 693.14/(2*0.166) = 2087.77 Hz

4) since f = (1/2L)*sqrt(T/mu)

to decrease the frequency tension T must be decreased

So the answer is decrease the tension

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