No, the speed of sound in air is not dependent on the frequency of the sound. The speed of sound in a given medium, such as air, is primarily determined by the properties of that medium, such as its density and elasticity.
In general, the speed of sound in air at room temperature is approximately 343 meters per second (or about 1,125 feet per second). This speed remains constant regardless of the frequency of the sound wave. Whether it's a high-frequency sound or a low-frequency sound, they will both travel at the same speed through the air under normal conditions.
However, what can vary with frequency is the way sound waves behave and interact with the environment. Higher frequency sound waves tend to have shorter wavelengths and can be more easily absorbed or scattered by obstacles in their path. This can lead to a decrease in their effective range as compared to lower frequency sound waves, which have longer wavelengths and can diffract around obstacles and travel over longer distances.
So, while the speed of sound remains constant regardless of frequency, the behavior and propagation characteristics of sound waves can vary depending on their frequency.