A number of strings of different densities are under tension. For each string yo

Question

A number of strings of different densities are under tension. For each string you measure the mass per unit length and the speed of transverse waves on the string.

Rank the following strings in order of their tension, from largest to smallest value.

1. Mass per unit length = .04 kg/m, speed of transverse waves = 40.0 m/s

2. mass per unit length = .0200 kg/m, speed of transverse waves = 80.0 m/s

3. mass per unit length = .0400 kg/m, speed of transverse waves = 20.0 m/s

4. mass per unit length = .0200 kg/m, speed of transverse waves = 40.0 m/s

5. mass per unit length = .0400 kg/m, speed of transverse waves = 80.0 m/s

Explanation / Answer

V^2 = T/u

or Tension T = V^2 * u

where u is called mass per unit length

1. T = 40*40 * 0.04 = 64 N

2. T = 80 *80 * 0.02 = 128 N

3. T = 20*20 * 0.04 = 16 N

4. T = 40*40* 0.02 = 32 N

5. T = 80*80* 0.04 =256 N

so order is

5> 2> 1> 4>3

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