Question

Spiders may "tune" strands of their webs to give enhanced response at frequencies corresponding to the frequencies at which desirable prey might struggle. Orb web silk has a typical diameter of 0.0020 mm, and spider silk has a density of 1300 kg/m3. To give a resonance at 100 Hz, to what tension must a spider adjust a 12-cm-long strand of silk?

Answer 1

0.00000313656610534 N

Step-by-step explanation:

`\rho` = Density of silk = 1300 kg/m³

d = Diameter = 0.002 mm

r = Radius = 0.001 mm

l = Length = 12 cm

f = Frequency = 100 Hz

Mass of the string is

`m=\rho V\\\Rightarrow m=\rho Al\\\Rightarrow m=1300* \pi (0.001* 10^(-3))^2* 0.12\\\Rightarrow m=4.9008845396* 10^(-10)\ kg`

Frequency is given by

`f=(1)/(2l)\sqrt{(T)/(m/l)}\\\Rightarrow T=4lf^2m\\\Rightarrow T=4* 0.16* 100^2* 4.9008845396* 10^(-10)\\\Rightarrow T=0.00000313656610534\ N`

The tension on the string is 0.00000313656610534 N