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A 2 g string, 0.76 m long, is under tension. The string produces a 900 Hz...

A 2 g string, 0.76 m long, is under tension. The string produces a 900 Hz tone when it vibrates in the third harmonic. The speed of sound in air is 344 m/s. The tension in the string, in SI units, is closest to:

(A) 740 (B) 650 (C) 450 (D) 550 (E) 350

I keep getting 456 as an answer-- which is incorrect. Please show work so I can see what I'm doing wrong. Thanks!

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Answer #1

m = mass = 2 g = 0.002 kg

L = length = 0.76 m

f3 = 900 Hz

V = 344 m/s

frequency for nth harmonic is given as

fn = (n/(2L)) sqrt(TL/m)

for n = 3

f3 = (3/(2L)) sqrt(TL/m)

900 = (3/(2 x 0.76)) sqrt(T (0.76)/0.002)

T = 547.2

on rounding

T = 550 N

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