Question 367: Waves

Question

A uniform wire $$20 \mathrm{~m}$$ long and weighing $$50 \mathrm{~N}$$ hangs vertically. The speed of the wave at mid point of the wire is (acceleration due to gravity $$=\mathrm{g}=10 \mathrm{~ms}^{-2}$$ )

Accepted Answer

$$\mathrm{m}=\frac{50}{10}=5 \mathrm{~kg}\quad$$ $$(\because \mathrm{W}=\mathrm{mg})$$
Tension in the mid-point of the wire is:
$$\mathrm{T}=\frac{\mathrm{m}}{2} \mathrm{~g}=\frac{5}{2} 	imes 10=25 \mathrm{~N}$$
$$	herefore \quad$$ Speed of the wave at mid-point of the wire is:
$$\begin{aligned}
\quad \mathrm{v} & =\sqrt{\frac{\mathrm{T}}{\mu}}=\sqrt{\frac{25}{\left(\frac{5}{20}ight)}} \quad\left(\because \mu=\frac{\mathrm{m}}{\mathrm{L}}ight) \
	herefore \quad \mathrm{v} & =10 \mathrm{~m} / \mathrm{s}
\end{aligned}$$

Answer

$$4 \mathrm{~ms}^{-1}$$

Answer

$$10 \sqrt{2} \mathrm{~ms}^{-1}$$

Answer

$$10 \mathrm{~ms}^{-1}$$

Answer

Zero $$\mathrm{ms}^{-1}$$

Waves

A uniform wire $20 \mathrm{~m} long and weighing 50 \mathrm{~N} hangs vertically. The speed of the wave at mid point of the wire is (acceleration due to gravity =\mathrm{g}=10 \mathrm{~ms}^{-2}$ )

Choose the correct answer: