Question

With what tension must a rope with length 2.30 mm and mass 0.105 kgkg be stretched for transverse waves of frequency 36.0 HzHz to have a wavelength of 0.790 mm?

Answer 1

Answer:

Tension must a rope be stretched is 36.8828 N

Explanation:

Wave speed in term of wavelength:

$v=f. \lambda$

Where:

f is the frequency

$\lambda$ is the wavelength

Now:

$v=36*0.790\\v=28.44 m/s$

Wave speed in term of tension force and mass per unit length

$v=\sqrt{\frac{F}{Mass\ per\ unit\ length}}$                          Eq (1)

Where:

F is the tension force

$Mass\ per\ unit\ length=\frac{0.105}{2.30} \\Mass\ per\ unit\ length=0.0456 Kg/m$

Since  $v$ is calculated above.On rearranging Eq (1) we will get:

$F=v^2 *Mass\ per\ unit\ length\\F=(28.44)^2*0.0456\\F=36.8828 N$

Tension must a rope be stretched is 36.8828 N