With what tension must a rope with length 3.40 m and mass 0.190 kg be stretched for transverse waves of frequency 42.0 Hz to have a wavelength of 0.850 m?

The tension is 71.27 N.

Explanation:

Tension of a rope can be found as the measure of product of square of velocity with linear density.

As the velocity of the object is product of frequency and wavelength. Similarly, the linear density is the measure of ratio of mass of the object per unit volume

Tension = (Velocity) ² * Linear density

Since, the length is given as 3.4 m, the mass is given as 0.190 kg, the frequency is given as 42 Hz and the wavelength is given as 0.850 m, then

Velocity = frequency * wavelength = 42 * 0.850 = 35.7

Linear density = Mass/Length = 0.190/3.40 = 0.056

Then, the tension = (35.7) ²*0.056 = 71.37 N.

So the tension is 71.27 N.