Question

Spacing between two successive nodes in a standing wave on a string is ${}^{\prime }x{}^{\prime }.$ If frequency of the standing wave is kept unchanged but tension in the string is doubled , then new spacing between successive nodes will become :

• A. $\frac{x}{\sqrt{2}}$
• B. $x\sqrt{2}$
• C. $\frac{x}{2}$
• D. $2x$

Answer 1

Answer: (B)

$x\sqrt{2}$

Wavelength of standing wave = $\lambda$

Frequency $=f$

Tension in string $=T$

Velocity of standing wave $=v=\sqrt{\frac{T}{\mu }}$

v = $\lambda f$

$\Rightarrow \lambda \propto \sqrt{T}$

Thus on doubling $T$:

${\lambda }_{new}=\sqrt{2}\lambda$

Spacing between 2 nodes = $\frac{\lambda }{2}$

Thus new spacing = $\sqrt{2x}$