Question 13 Marks
A steel wire has a length of 12.0 m and a mass of 2.10 kg. What should be the tension in the wire so that speed of a transverse wave on the wire equals the speed of sound in dry air at 20°C = 343 ms–1?
Answer
View full question & answer→Length of steel wire = 12.0 meter
Mass $(M)=2.10 kg$, Tension in wire $T =$ ?
Unit length mass of wire
$m=\frac{M}{l}=\frac{2.10}{12.0}=0.175 kg / m$
Speed of sound in dry air $=343 m / s$
We know that $\quad v =\sqrt{\frac{ T }{m}}$
or $\quad$$v^2=\frac{T}{m}$
or$\quad$$T=v^2 m$
Put the value $\quad=(343)^2 \times 0.175$
$=343 \times 343 \times 0.175 $
$=2.06 \times 10^4 N$
Mass $(M)=2.10 kg$, Tension in wire $T =$ ?
Unit length mass of wire
$m=\frac{M}{l}=\frac{2.10}{12.0}=0.175 kg / m$
Speed of sound in dry air $=343 m / s$
We know that $\quad v =\sqrt{\frac{ T }{m}}$
or $\quad$$v^2=\frac{T}{m}$
or$\quad$$T=v^2 m$
Put the value $\quad=(343)^2 \times 0.175$
$=343 \times 343 \times 0.175 $
$=2.06 \times 10^4 N$


