No, all frequencies do not travel at the same speed in air, water, or other mediums. The speed of sound varies with the properties of the medium through which it travels, including factors such as density, elasticity, and temperature.
In general, the speed of sound in a medium increases with increasing elasticity and decreases with increasing density. This means that different frequencies can have slightly different speeds of propagation within the same medium.
In air, for example, the speed of sound is influenced by factors such as temperature and humidity. Under normal conditions, at room temperature and sea level, the speed of sound in dry air is approximately 343 meters per second (1,125 feet per second). However, this value can change with variations in temperature and humidity.
Regarding different frequencies, lower frequency sound waves tend to travel slightly faster than higher frequency waves in the same medium. This phenomenon is known as dispersion. It occurs because the speed of sound depends on how quickly the molecules or particles in the medium can respond to changes in pressure. Lower frequency waves cause slower oscillations, allowing the medium to respond more easily and resulting in a slightly higher speed.
In mediums such as water and metal, the speed of sound is also influenced by their specific properties. For instance, sound waves travel faster in water than in air, with a speed of approximately 1,480 meters per second (4,850 feet per second) at room temperature. In metals, sound waves can propagate even faster due to the high elasticity of the material.
However, it's important to note that the speed of sound can still vary with frequency within a particular medium. Dispersion effects can cause slight differences in the speed of propagation for different frequencies, although the variation is typically small.
In summary, the speed of sound depends on the properties of the medium, and while all frequencies share a similar speed range within a medium, slight variations can occur due to factors like dispersion and the medium's specific characteristics.