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What is the fundamental frequency of a guitar string that is 1 m long, the mass per...

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alicesmith | Student, Grade 9 | (Level 1) Salutatorian

Posted October 11, 2010 at 4:32 AM via web

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What is the fundamental frequency of a guitar string that is 1 m long, the mass per unit length is 50 g/m and the Tension in the string is 50 N.

 

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william1941 | College Teacher | (Level 3) Valedictorian

Posted October 11, 2010 at 4:33 AM (Answer #1)

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We have to find the fundamental frequency of a string. The formula for the fundamental frequency of a stretched string is given by

sqrt [ T/ (m/L)]/ 2*L , where T is the tension in the string, m is the mass per length and L is the length of the string.

Using the values given to us:

L = 1m

m= 50g /m = .05 Kg/m

T = 50 N

Therefore sqrt [ T/ (m/L)]/ 2*L

=> sqrt [ 50/ (.05/1)]/ 2*1

=> sqrt [ 50 / .05] / 2

=> sqrt 1000 /2

=> 31.62 / 2

=> 15.81 Hz

Therefore the fundamental frequency is 15.81 Hz

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ndnordic | High School Teacher | (Level 2) Associate Educator

Posted October 11, 2010 at 10:58 AM (Answer #2)

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An alternate method is to recognize that for a string fixed at both ends the wavelength is 2 times the length of the string.  In that case you have a wavelength of 2 m.

The relationship between the string tension F(T), the m/L ratio and the velocity of the wave is:  F(T) = m/L * v^2

Solving for the velocity gives 31.62 m/s.

Since v = frequency * wavelength;  31.62 m/s  divided by 2 m = 15.81  Hz as the fundamental frequency.

As you can see, in physics there is often more than one way to end up with the correct answer.

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