Imagine that a string on an acoustic guitar is 25inches longbetween its fixed en

Question

Imagine that a string on an acoustic guitar is 25inches longbetween its fixed ends. According to example E15.2, the speedof waves on a stretched strig isv=(FT/). The highest E string on sucha guitar has a pitch of about 329Hz. Assume that theparticular string used has a mass per unit length of=0.2g/m.
a)What tension force must be applied to this string? b)By what fraction would we have to increase the tension totune the string up to G (392 Hz)? Imagine that a string on an acoustic guitar is 25inches longbetween its fixed ends. According to example E15.2, the speedof waves on a stretched strig isv=(FT/). The highest E string on sucha guitar has a pitch of about 329Hz. Assume that theparticular string used has a mass per unit length of=0.2g/m.
a)What tension force must be applied to this string? b)By what fraction would we have to increase the tension totune the string up to G (392 Hz)?

Explanation / Answer

We know frequency f = ( 1/ 2L ) [ T / ] where L = length = 25 inches = 25 * 2.54 cm             = 63.5 cm = 0.635 m           T =tension            f= 329 Hz           = mass per unit length of =0.2g/m              = 0.2 * 10 -3 kg / m from this Tension   T = 4L 2 f2 substitue values weget answer (b). we know f T from this ( f / f ' ) = {T / T ' } given f = 329 Hz          f ' = 392Hz          T =T    it is calculates in above problem          T ' = ? from above T ' = T ( f ' / f ) 2 substitue values weget answer substitue values weget answer

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