Speed of Wave on String — Prelims Strategy

Prelims Strategy

To effectively tackle NEET questions on the speed of waves on a string, a clear strategy is essential. Firstly, memorize the core formula $v = \sqrt{T/\mu}$ and understand the meaning and units of each term.

For numerical problems, always ensure all quantities are in SI units (T in Newtons, $\mu$ in kg/m, $v$ in m/s). Pay close attention to unit conversions, especially for mass (grams to kilograms) and length (cm to m).

When dealing with ratio-based problems, write down the initial and final states, and use ratios like $v_2/v_1 = \sqrt{T_2/T_1} \cdot \sqrt{\mu_1/\mu_2}$ to simplify calculations and avoid repetitive steps.

For conceptual questions, remember that wave speed is an intrinsic property of the medium, determined by tension and linear mass density, and is independent of the wave's amplitude or frequency. Be wary of trap options that suggest a linear relationship or dependence on amplitude/frequency.

If tension is due to a hanging mass, remember $T=Mg$. For vertically suspended strings, tension varies with position, so calculate $T$ at the specific point of interest. Practice a variety of problems, including those involving changes in string material (affecting $\mu$ via density and radius) and those combining $v = f\lambda$ with $v = \sqrt{T/\mu}$.