UPSC NDA I 2023 General Ability Solved Paper

Concept:In a given medium under the same physical conditions, the speed of sound is independent of the frequency of the sound wave. It depends only on the properties of the medium (such as density, elasticity, and temperature).Explanation:The speed of sound in a gaseous medium is given by the formula: $v = \sqrt{\frac{\gamma P}{\rho}}$ where $P$ is the pressure, $\rho$ is the density, and $\gamma$ is the ratio of specific heats of the gas.This formula does not contain any term for frequency, so the speed remains constant for all frequencies in a given medium under identical physical conditions.When the frequency changes, the wavelength adjusts accordingly because $v = f \lambda$ (speed = frequency × wavelength).Thus, higher frequency leads to shorter wavelength, but speed does not change.Options B and C claim speed changes with frequency; both are incorrect.Option D claims speed is slower at higher wavelengths; that is also incorrect, as speed is independent of wavelength.Therefore, the correct statement is that the speed of sound remains the same at all frequencies in a given medium.Answer:Option A: Speed of sound remains same at all frequencies.