Respuesta :
Explanation:
Formula for wave velocity is as follows.
[tex]\nu = \sqrt{\frac{T}{\frac{m}{L}}}[/tex] .......... (1)
Now, we know that relation between velocity and frequency is as follows.
f = [tex]\frac{\nu}{2L}[/tex] ......... (2)
Now, on equating equation (2) in equation (1) is as follows.
f = [tex]\frac{\sqrt{\frac{T}{\frac{m}{L}}}}{2L}[/tex]
We will calculate the mass with the help of relation between density and volume as follows.
Density [tex](\rho) = \frac{m}{V}[/tex]
m = [tex]\rho (AL)[/tex]
= [tex]1300 kg/m^{3} \times \frac{0.002 \times 10^{-3}}{2} \times 3.14 \times 0.14[/tex]
= [tex]5.71 \times 10^{-10} kg[/tex]
Now, we will rewrite the equation f = [tex]\frac{\sqrt{\frac{T}{\frac{m}{L}}}}{2L}[/tex] for T as follows.
[tex](2Lf)^{2} = \frac{T}{\frac{m}{L}}[/tex]
T = [tex]\frac{m}{L} (2Lf)^{2}[/tex]
= [tex][\frac{5.71 \times 10^{-10} kg}{0.16 m}](2 (0.16 m)(100 Hz))^{2}[/tex]
= [tex]3.65 \times 10^{-6} N[/tex]
thus, we can conclude that up to [tex]3.65 \times 10^{-6} N[/tex] tension must a spider adjust a 16cm long strand of silk.
