No, sound waves of different frequencies do not necessarily have the same speed. The speed of sound in a medium depends on the properties of the medium itself, such as its density, elasticity, and temperature.
In general, in a given medium, sound waves of different frequencies will propagate at the same speed. This is true for idealized situations where the medium is homogeneous and at a uniform temperature. In such cases, all sound waves, regardless of their frequency, will travel at the same speed.
However, in real-world scenarios, the speed of sound can vary with frequency due to various factors. For example, in certain media like gases, the speed of sound can depend on the frequency due to the presence of molecular interactions or the temperature dependence of the gas properties. This phenomenon is known as dispersion.
In solids, the speed of sound can also be frequency-dependent due to the complex interaction of the wave with the crystal lattice structure, resulting in different speeds for different modes of vibration.
So, while the speed of sound is often assumed to be the same for all frequencies in simplified models, it can indeed vary in practical situations depending on the characteristics of the medium and the specific frequency range being considered.