Problem 12.19 Copy The portion of string between the bridge and uppe end of the

Question

Problem 12.19 Copy The portion of string between the bridge and uppe end of the fingerboard (the part of the string that is free to vibrate) of a certain musical instrument is 60.0 cm long and has a mass of 2.10g. The string sounds an A4 note (440 Hz) when played. Figure 1 of 1 Finger board 60.0 cm Bridge Part A Where must the player put a finger at what distance a from the bridge to play a D5 note (587 Hz)? (See the figure (Figure 1) Fo both notes, the string vibrates in its fundamental mode. z> 0.45 Cm. Submit My Answers Give U Incorrect, Try Again, 5 attempts remaining Part B Withou etuning, is it possible to play a G4 note (392 Hz on this string? No, it's impossible to play Submit My Answers Give Up Correct

Explanation / Answer

part A )

let the tension in the string is T

Now, for frequency , f = 440 Hz

f = sqrt(T*L/m)/2L

440 = sqrt(T*0.60/.0021)/(2 * 0.60)

solving for T

T = 975.74 N

Now, for frequency , f = 587 Hz

let the length distance from bridge is x

587 = sqrt(975.74*(x)/.0021)/(2 * ( x))

x = 0.337 = 33.7 cm

the distance from the bridge is 33.7 cm

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