Question

With what tension must a rope with length 3.00 mm and mass 0.105 kgkg be stretched for transverse waves of frequency 40.0 HzHz to have a wavelength of 0.790 mm

Answer 1

the tension of the rope is 34.95 N

Step-by-step explanation:

Given;

length of the rope, L = 3 m

mass of the rope, m = 0.105 kg

frequency of the wave, f = 40 Hz

wavelength of the wave, λ = 0.79 m

Let the tension of the rope = T

The speed of the wave is given as;

`v = f\lambda = \sqrt{(T)/(\mu) } \\\\where;\\\\\mu \ is \ mass \ per \ unit \ length\\\\\mu = (0.105)/(3) = 0.035 \ kg/m\\\\v = f\lambda = 40 * 0.79 = 31.6 \ m/s\\\\v = \sqrt{(T)/(\mu) } \\\\v^2 = (T)/(\mu) \\\\T = v^2 \mu\\\\T = (31.6^2)(0.035)\\\\T = 34.95 \ N`

Therefore, the tension of the rope is 34.95 N