The problem with the graph above is that it gives an example with descriptions that do not reflect the physical reality and are threfore misleading.
E.g. the first picture doesn't show a "recorded deep bass sound" but an impulse which when transformed into the frequency domain via Fourier transform would have infinite spectrum width (so a lot of high frequencies too!).
Remember that any time-domain function can be transformed into an equivalent frequency (magnitude + phase) response and vice-versa. I.e. the impulse and frequency responses of the same system show the same data - just a different view of it.
This can be difficult to explain in just a few words and without math - but there are e.g. some nice visual explanations on ASR and elsewhere.
In addition, it appears humans are in general far more sensitive to small frequency response magnitude differences than many phase or time domain differences. This means that in controlled blind tests people often wouldn't be able to reliably differentiate between sounds with the same frequency magnitude spectrums but different time domain function shapes (within reason, of course).
Many times the feeling of "speed" relates simply to the lack of bass resonance peaks, or less bass, or more treble, or some combination of these.
Hope this helps!
EDIT: Let me provide some references, perhaps it will be helpful to some!
- Link to an AudioXpress article on audibility of phase with comments from Dr. Floyd Toole, Dr. Wolfgang Klippel, Andrew Jones and James Croft
- Link to ASR post #1 - Illustrations of how high-passing or low-passing and ideal pulse impacts the signal in frequency and time domain. Also an illustration of how the step and impulse response looks like when limited to the human hearing range (20Hz-20kHz) in an idealized case.
- Link to ASR post #2 - Illustration of how typical loudspeaker crossover impacts the impulse and step response, comparison between a real loudspeaker response and a similar idealized simulated response.
- Link to ASR post #3 - A very nice illustration showing how a sum of 3 sine waves of different frequencies looks like in the time and frequency domains (Fourier transform)