With what tension must a rope with length 2.90 m and mass 0.125 kg be stretched for transverse waves of frequency 42.0 Hz to have a wavelength of 0.740 m

41.64 N

Explanation:

Applying,

v = √(T/m') Equation 1

Where v = velocity of the wave, T = Tension of the rope, m' = mass per unit length of the rope.

make T the subject of the equation,

T = v²m' Equation 2

But,

v = λf Equation 3

Where λ = wavelength, f = frequency

And

m' = m/L Equation 4

Where m = mass of the rope, L = length of the rope

Substitute equation 3 and equation 4 into equation 2

T = (λf)²(m/L) Equation 5

From the question,

Given: λ = 0.740 m, f = 42 Hz, m = 0.125 kg, L = 2.9 m

Substitute these values into equation 5

T = (42×0.74)²(0.125/2.9)

T = 41.64 N

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