Question

the pulse in the figure shown has a speed of 0.1 $m{s}^{-1}$. the linear mass density of the right string is 0.25 that of the left string. At what speed does the transmitted wave travel ?

• A. $25cm{s}^{-1}$
• B. $20cm{s}^{-1}$
• C. $15cm{s}^{-1}$
• D. $17.5cm{s}^{-1}$

Answer 1

The correct option is B $20cm{s}^{-1}$

Given,

String tension is same.

$V_{left}=0.1m/s$

${\mu }_{left}=1kg/m^3$

${\mu }_{right}=0.25kg/m^3$

The speed of wave in the left part of string,

$V=\sqrt{\frac{T}{\mu }}$. . . . . . . .(1)

From the above equation,

$\frac{V_{right}}{V_{left}}=\sqrt{\frac{{\mu }_{left}}{{\mu }_{right}}}=\sqrt{\frac{1}{0.25}}$

$V_{right}=2V_{left}=2\times 0.1=0.2m/s$

$V_{right}=20cm/s$

The correct option is B.