What evidence can you give that the speed of sound in air does not depend significantly on frequency?
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You can see in the picture below the illustration of a low frequency sound.
You can see in the picture below wave illustration of higher frequency sound.
The frequency of the sound is changed from the source; the higher vibration of the source produces higher frequency of the sound. It doesn’t affect the speed of the sound waves, Speed of the sound waves depend only on the properties of the medium that the sound travels in.
For example. The sound waves are faster in hot air than cold air.
The higher frequency sound and lower frequency sound reaches the listener at the same time.