One end of a stretched rope is given a periodic transverse motion with a frequency of $10 \mathrm{Hz}$. The rope is $50 \mathrm{m}$ long, has total mass $0.5 \mathrm{kg}$ and is stretched with a tension of $400 \mathrm{N}$.

(a) Find wave speed and wavelength.

One end of a stretched rope is given a periodic transverse motion with a frequency of $10 \mathrm{Hz}$. The rope is $50 \mathrm{m}$ long, has total mass $0.5 \mathrm{kg}$ and is stretched with a tension of $400 \mathrm{N}$.

(b) If the tension is doubled, how must the frequency be changed to maintain the same wavelength?

A metal wire has these properties. Coefficient of linear expansion $1.5\times {10}^{-5}{\left({}^0\mathrm{C}\right)}^{-1}$

Young's modulus $=2.0\times {10}^{11} \mathrm{Pa}$

Density $=9.0\times {10}^3 \mathrm{kg}/{\mathrm{m}}^3$

At each end there are rigid supports. If the tension is zero at $20°\mathrm{C}$, what will be the speed of a transverse wave at $8°\mathrm{C}$.