Question

Tension is maintained in a string as in the figure below. The observed wave speed is 23 m/s when the suspended mass is 3.0 kg.

(a) What is the mass per unit length of the string?

kg/m?

(b) What is the wave speed when the suspended mass is 2.5 kg?

m/s?

Answer 1

The speed of the wave in astretched string is given by

                     v=√(T/m)

v is the speed of the wave = 23 m/s

T is the tension applied = mg

                                    = 3 kg * 9.8 m/s^2

                                   = 29.4 N

Then the linear density of the string is given by m = T/v^2

                                                                            = 29.4 N / 23 m/s*23 m/s

                                                                            = 0.0556 kg/m

If the attached mass is replace by 2.5 kg

Then the tension applied is T = 2.5 kg * 9.8 m/s^2

                                            = 24.5 N

Now the wave speed in the same string is given by

                                      v = √(T/m)

                                         = √(24.5 N / 0.0556 kg/m )

                                         = 20.99 m/s