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A 2-g string that is 0.79 m long is fixed at both ends and is under tension. This string produces a 500-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 __________

Respuesta :

Answer:

[tex]T = 175.6 N[/tex]

Explanation:

As we know that string is vibrating in third harmonic

So we will have

[tex]L = 3\frac{\lambda}{2}[/tex]

so we have

[tex]0.79 = \frac{3}{2}\lambda[/tex]

so we have

[tex]\lambda = \frac{2}{3}(0.79)[/tex]

[tex]\lambda = 0.527[/tex]

we know that frequency of the wave is given as

f = 500 Hz

now we know that

speed of the wave is

[tex]v = frequency \times wavelength[/tex]

[tex]v = (500)(0.527)[/tex]

[tex]v = 263.3 m/s[/tex]

now we have

[tex]v = \sqrt{\frac{T}{m/L}}[/tex]

so we have

[tex]263.3 \sqrt{\frac{T}{(0.002/0.79)}}[/tex]

[tex]T = 175.6 N[/tex]