In general, sound waves of different frequencies do have the same speed in a given medium. The speed of sound in a particular material depends on the properties of that material, such as its density and elasticity. For a specific medium, the speed of sound remains relatively constant regardless of the frequency of the sound waves passing through it.
However, it's worth noting that in certain cases, the speed of sound may vary slightly with frequency due to effects such as dispersion. Dispersion is the phenomenon where the speed of sound can vary with frequency, causing different frequencies to propagate at slightly different speeds. This effect is more prominent in complex media, such as in dispersive materials or in waveguides with frequency-dependent properties.
In most common materials and everyday situations, however, the speed of sound is considered frequency-independent, and all audible frequencies travel at the same speed through a given medium.