What should be the tension applied to a wire of length 1 m and mass 10

1.	What should be the tension applied to a wire of length 1 m and mass 10 grams, if it has to vibrate with the fundamental frequency of 50 Hz ?
Answer» Data : L = 1 m, mass of the wire = 10 g = 0.01 kg, n = 50 Hz ∴ m = mass per unit length of the wire = \(\frac{0.01}1\) = 0.01 kg/m n = \(\frac 1{2L}\)\(\sqrt{\frac Tm}\) ∴ Tension = T = 4n²L² m = 40(50)² (1)² (0.01) = 4 × 2500 × 0.01 = 100 N

What should be the tension applied to a wire of length 1 m and mass 10 grams, if it has to vibrate with the fundamental frequency of 50 Hz ?

Answer»

Data : L = 1 m, mass of the wire = 10 g = 0.01 kg, n = 50 Hz

∴ m = mass per unit length of the wire = \(\frac{0.01}1\) = 0.01 kg/m

n = \(\frac 1{2L}\)\(\sqrt{\frac Tm}\)

∴ Tension = T = 4n²L² m

= 40(50)² (1)² (0.01)

= 4 × 2500 × 0.01 = 100 N