Question 164: Waves

Question

A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block
of mass 2 kg is attached to its free end. A transverse short wavetrain of wavelength 6 cm is
produced at the lower end of the rope. What is the wavelength of the wavetrain (in cm) when it
reaches the top of the rope ?

Accepted Answer

T
1
= 2g
T
2
= 8g
V = $$\sqrt {{T \over \mu }} $$
$$ 	herefore $$ V $$ \propto $$ $$\sqrt T $$
Also V = f$$\lambda $$
$$ 	herefore $$ V
1
= f
1
$$\lambda $$
1
and V
2
= f
2
$$\lambda $$
2
We know frequency of sources are same.
$$ 	herefore $$ f
1
= f
2
So $$\sqrt {{{{T_1}} \over {{T_2}}}}  = {{{\lambda _1}} \over {{\lambda _2}}}$$
$$ \Rightarrow $$ $$\sqrt {{{2g} \over {8g}}}  = {6 \over {{\lambda _2}}}$$
$$ \Rightarrow $$ $$\lambda $$
2
= 12 cm

Answer

12

Answer

3

Answer

9

Answer

6

Waves

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