A string has tension \(80\,\mathrm{N}\) and linear density \(0.020\,\mathrm{kg\,m^{-1}}\). Find the wave speed.

If the tension in a string is quadrupled while the linear density stays constant, by what factor does the wave speed change?

If the linear density of a string is increased by a factor of \(9\) while the tension stays constant, by what factor does the wave speed change?

A string carries waves at \(50\,\mathrm{m\,s^{-1}}\) under tension \(125\,\mathrm{N}\). Find its linear density.

Two strings are under the same tension. String A has linear density \(0.010\,\mathrm{kg\,m^{-1}}\) and string B has \(0.040\,\mathrm{kg\,m^{-1}}\). Compare their wave speeds.

Show from units alone that \(T/\mu\) has the dimensions of speed squared.

A string of fixed mass is stretched so its length doubles while the tension quadruples. By what factor does the transverse wave speed change?

A string has fixed mass \(M\) and original length \(L\). It is stretched to a new length \(\alpha L\). Find the tension required, in terms of the original tension \(T_0\), to keep the wave speed unchanged. Then find the tension required to double the original wave speed.