Question

A string of length 20 cm and linear mass density $0.40gc{m}^{-1}$ is fixed at both ends and is kept under a tension of 16N. A wave pulse is produced at t = 0 near an end as shown in figure, which travels towards the otherend. When will the string have the shape shown in the figure again?

• A. 0.1 sec
• B. 0.02sec
• C. 0.5sec
• D. 2sec

Answer 1

The correct option is B

0.02sec

Given l = 20 cm = 0.2 m

$\mu =0.40gc{m}^{-1}$

$0.4\times {10}^{-1}kg{m}^{-1}$

$F=16N$

$v=\sqrt{\frac{F}{\mu }}=\sqrt{\frac{16}{0.4\times {10}^{-1}}}=20m/s$

The wave will hit the fixed end and be reflected.

The reflected wave will be out of phase and will come back to the starting wall and get reflected again

Now the wave looks like when it started. So how long has it travelled to be here twice the length of the string.

$2l=40cm$

Speed = $20m/s$

So time = $\frac{40\times {10}^{-2}}{20}=2\times {10}^{-2}=0.02sec$