Question

How does speed of sound in air depend on the frequency of sound?

Answer 1

No. The frequency is set by the oscillating body which sets up the sound waves. The speed of the waves is determined by the elastic/inertial properties of medium and the wavelength is then given by λ = v/f. As a practical example, think about an orchestra. If v did vary with f, the sounds from the different instruments would reach your ears at different times. The result would not be very musical.
An increase in wave frequency caused a decrease in wavelength while the wave speed remained constant.