Question

On a string, the space between nodes is 5 cm. The transverse wave has a velocity of 2 ms -1. The frequency is then

• A. $5\mathrm{Hz}$
• B. $10\mathrm{Hz}$
• C. $20\mathrm{Hz}$
• D. $15\mathrm{Hz}$

Answer 1

The correct option is C

$20\mathrm{Hz}$

Step: 1 Given data:

Distance between two nodes = $5\mathrm{cm}$.

The velocity of a transverse wave $\left(\mathrm{v}\right)=2{\mathrm{ms}}^{-1}$.

Step: 2 Formula used:

The distance between two nodes $=\frac{\mathrm{\lambda }}{2}$.

Frequency $\left(\mathrm{f}\right)=\frac{\mathrm{v}}{\mathrm{\lambda }}$

Step: 3 Solve for frequency:

Distance between two nodes $=\frac{\mathrm{\lambda }}{2}$.

Therefore, $\frac{\mathrm{\lambda }}{2}=5$

$\mathrm{\lambda }=10\mathrm{cm}\mathrm{or}0.1\mathrm{m}$

Frequency $\left(\mathrm{f}\right)=\frac{\mathrm{v}}{\mathrm{\lambda }}=\frac{2}{0.1}$

$=20\mathrm{Hz}$

Hence, option C is correct.