Question

A wire is made by welding together two metals having different densities. Figure shows a $2.00m$ long section of wire centered on the junction, but the wire extends much farther in both directions. The wire is placed under $2250N$ tension, then a $1500Hz$ wave with an amplitude of $3.00mm$ is sent down the wire. How many wavelengths (complete cycles) of the wave are in this $2.00m$ long section of the wire?

Answer 1

Answer: 8

$v_1=\sqrt{\frac{T_1}{{\mu }_1}}=\sqrt{\frac{2250\times 10^3}{900}}$
$=5\times 100=500m/s$
$v_2=\sqrt{\frac{T_2}{{\mu }_2}}=\sqrt{\frac{2250\times 10^3}{25}}$
$=3\times 100=300m/s$
${\lambda }_1=\frac{v_1}{f}{\lambda }_2=\frac{v_2}{f}$
${\lambda }_1=\frac{1}{3}m$
${\lambda }_2=\frac{1}{5}m$
$\therefore$ Net wavelength $=3+5=8$