Often, then, when scientists characterize the response of a shift-invariant linear system they will not tell you the impulse response. Rather, they will give you plots that tell you about the values of the shift and scale for each of the possible input frequencies. This representation of how the shift-invariant linear system behaves is equivalent to providing you with the impulse response function. We can use these numbers to compute the response to any stimulus. If you know the responses for sine waves of all frequencies, then you can determine how the system will respond to any possible periodic stimulus.
Many people find the characterization in terms of frequency response to be intuitive.
And most of you have seen graphs that describe systems this way. Stereo systems, for example, are pretty good shift-invariant linear systems. They can be evaluated by measuring the signal at different frequencies. And the stereo controls are designed around the frequency representation. Adjusting the bass alters the level of the low frequency signals, while adjusting the treble adjust the level of the high frequency signals.