Question

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

Answer 1

$v_{1}=\sqrt{\frac{T_{1}}{\mu_{1}}}=\sqrt{\frac{2250 \times 10^{3}}{900}}$
$=5 \times 100=500 \,m / s$
$v_{2}=\sqrt{\frac{T_{2}}{\mu_{2}}}=\sqrt{\frac{2250 \times 10^{3}}{25}}$
$=3 \times 100=300\, m / s$
$\lambda_{1}=\frac{v_{1}}{f} \lambda_{2}=\frac{v_{2}}{f}$
$\lambda_{1}=\frac{1}{3} m$
$\lambda_{2}=\frac{1}{5} m$
$\therefore $ Net wavelength $=3+5=8$