Question 415: Waves

Question

A uniform rope of length $$12 \mathrm{~m}$$ and mass $$6 \mathrm{~kg}$$ hangs vertically from the rigid support. A block of mass $$2 \mathrm{~kg}$$ is attached to the free end of the rope. A transverse pulse of wavelength $$0.06 \mathrm{~m}$$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is

Accepted Answer

Speed of a wave in a string is given by
$$\begin{aligned}
& V=n \lambda=\sqrt{\frac{T}{m}} \
& 	herefore \lambda=\frac{1}{n} \sqrt{\frac{\mathrm{T}}{\mathrm{m}}} \
& 	herefore \frac{\lambda_2}{\lambda_1}=\sqrt{\frac{\mathrm{T}_2}{\mathrm{~T}_1}}
\end{aligned}$$
Tension at the bottom of the rope $$=\mathrm{T}_1=2 \mathrm{~kg}$$
Tension at the top of the rope $$\mathrm{T}_2=2+6=8 \mathrm{~kg}$$
$$\begin{aligned}
	herefore \lambda_2 & =\sqrt{\frac{T_2}{T_1}} \cdot \lambda_1=\sqrt{\frac{8}{2}} 	imes 0.06 \
& =2 	imes 0.06=0.12 \mathrm{~m}
\end{aligned}$$

Answer

$$0.8 \mathrm{~m}$$

Answer

$$0.16 \mathrm{~m}$$

Answer

$$0.12 \mathrm{~m}$$

Answer

$$0.4 \mathrm{~m}$$

Waves

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