Which one among the following is true for the speed of sound in a give

Which one among the following is true for the speed of sound in a given medium ?

Speed of sound remains same at all frequencies
Speed of sound is faster at higher frequencies
Speed of sound is slower at higher frequencies
Speed of sound is slower at higher wavelengths
This question was previously asked in
UPSC NDA-1 – 2023
The speed of sound in a given medium is primarily determined by the properties of the medium itself, such as its elasticity (or compressibility) and density. In a specific medium under uniform conditions (like constant temperature and pressure for air), the speed of sound is generally constant and independent of the frequency or wavelength of the sound wave. The relationship v = fλ (speed = frequency × wavelength) holds true, meaning that if the frequency changes, the wavelength changes accordingly to keep the speed constant.
– Speed of sound depends on the properties of the medium (elasticity and density).
– For a given medium under specific conditions, the speed of sound is constant.
– The relationship v = fλ implies an inverse relationship between frequency (f) and wavelength (λ) for a constant speed (v).
– In contrast, for light waves in a *dispersive* medium (like glass), speed *does* depend on frequency/wavelength. However, for sound waves in typical media like air, water, or solids, dispersion effects related to frequency are usually negligible unless considering very specific materials or high frequencies outside the audible range.
Factors that affect the speed of sound in air include temperature (speed increases with temperature), humidity (speed increases slightly with humidity), and pressure (for an ideal gas, speed is independent of pressure at constant temperature and density). The speed of sound is generally fastest in solids, slower in liquids, and slowest in gases.
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