Question

-g With what tension must a rope with length 2.50 m and mass 0.120 kg be stretched for transverse waves of frequency 40.0 Hz to have a wavelength of 0.750 m?

Answer 1

Answer:

43.2 N

Explanation:

$\lambda$ = Wavelength = 0.75 m

f = Frequency = 40 Hz

m = Mass of string = 0.12 kg

L = Length of string = 2.5 m

$\mu$ = Linear density = $\dfrac{m}{L}$

Velocity of wave is given by

$v=\lambda f\\\Rightarrow v=0.75\times 40\\\Rightarrow v=30\ m/s$

The tension in string is given by

$T=v^2\mu\\\Rightarrow T=30^2\times \dfrac{0.12}{2.5}\\\Rightarrow T=43.2\ N$

The tension in the string is 43.2 N