Question

A string of length $1m$ and mass $5g$ is fixed at both ends. The tension in the string is $8.0N$. The string is set into vibration using an external vibrator of frequency $100Hz$. The separation between successive nodes on the string is close to__?

• A. $16.6cm$
• B. $20.0cm$
• C. $10.0cm$
• D. $33.3cm$

Answer 1

The correct option is B $20.0cm$

Velocity of wave on string
$V=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{8}{5}\times 1000}=40m/s$
Now, wavelength of wave $\lambda =\frac{v}{n}=\frac{40}{100}m$
Separation b/w successive nodes, $\frac{\lambda }{2}=\frac{20}{100}m$
$=20cm$.