Question

With what tension must a rope with length 3.40 m and mass 0.150 kg be stretched for transverse waves of frequency 50.0 Hz to have a wavelength of 0.850 m ?

Answer 1

Concepts and reason

The concept used to solve this problem is standing wave in a string and tension force.

First use the relation between frequency and wavelength to calculate the speed of the wave in the string.

Finally use the relationship between speed of the wave of the string, length of the string, and mass of the string to calculate the required tension.

Fundamentals

Expression for the speed of the wave in the string is,

$v=f2 $

Here, v is the speed of the wire in the string, f is the frequency of the wave, and is the wavelength.

Expression for the linear density is,

Here, is the linear density, m is the mass, and l is the length of the string.

Expression for the speed of the wave in terms of tension and linear density is,

Substitute for .

Rearrange the above equation to get the required tension,

Expression for the speed of the wave in the string is,

$v=f2 $

Substitute for f and for .

Expression for the required tension is,

Substitute for v, for , and for .

Ans:

The required tension is .