CHAPTER $15$ SYNTHESIS PROBLEMS

SP$1$

A certain rope has a length of $8$ m and a mass of $2\mathrm{.}4$ kg $.$ It is fixed at one end and held taut at the other with a tension of $30$ N $.$ The end of the rope is moved up and down with a frequency of $2\mathrm{.}5$ Hz $.$

a$.$ What is the mass per unit of length of the rope?

b$.$ What is the speed of waves on this rope?

c$.$ What is the wavelength of waves on this rope having a frequency of $2\mathrm{.}5$ Hz $?$

d$.$ How many complete cycles of these waves will fit on the rope?

e$.$ How long does it take for the leading edge of the waves to reach the other end of the rope and start coming back?