Question

A5-g string that is 0.56 m long is fixed at both ends and is under tension. This string produces a 800 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 is closest to O 510 N. O 650 N. 800 N O 940 N. 0 1100 N. Submit Request Answer Provide Feedback Next >

Answer 1

Given that string produces 800 Hz tone when vibrates in the third harmonic,

L = length of string = 0.56 m

Now wavelength of 3rd harmonic will be:

$\lambda$ = 2L/3 = 2*0.56/3 = 0.3733 m

Now wave speed on the string is also given by:

V = sqrt (T/$\mu$)

$\mu$ = mass per unit length = m/L

V = wave speed = f3*$\lambda$

V = 800*0.3733 = 298.64 m/s

So,

T = V^2*$\mu$ = m*V^2/L

m = mass of string = 5 gm = 5.0*10^-3 kg

Using given values:

T = 5*10^-3*298.64^2/0.56

T = 796.30 N = 800 N

Correct option is C.