Question

The pulse shown in figure has a speed of $10cm/s$. If the linear mass density of the right string is $0.25$ that of the left string, at what speed does the transmitted pulse travel ?

• A. $20cm/s$
  
• B. $10cm/s$
  
• C. $60cm/s$
  
• D. $50cm/s$
  

Answer 1

The correct option is A $20cm/s$

The tension throughout the string remains the same.
The speed of wave in the left part of string $=v_{left}=\sqrt{\frac{T}{{\mu }_{left}}}=10cm/s$

The speed of wave in the right part of string $=v_{right}=\sqrt{\frac{T}{{\mu }_{right}}}$

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

$⟹v_{right}=2\times v_{left}$$=20cm/s$