Help understanding impulse response
Firstly, for a response to be classified as the response to an impulse. The input first must qualify as an impulse to the system. For ex: a quick clap could be the impulse input to measure the sound impulse response of the room.

In your case, hitting the hammer at point E must be a "good enough" impulse input for all the materials and lengths.

The issue however is complicated in this case as locations A and B are simply outputs when viewed inline with systems theory for the rope system you constructed. Therefore, the excitation at input should be an "effective impulse" at both locations A and B for you to effectively denote the response of both sensors at A and B to be the response of an impulse.

So the essential question here is to first classify what qualifies as an impulse for rope at E and the suseuqent uniformity of excitation across the length.

If the excitation  at E is not uniform at A and B then you would have to define two effective impulses for your rope system. One for the response at A and other at B.

Once you know the impulse response. Then any input can be written as sum of weighted impulses and if the system is linear and time invariant then the output is simply the sum of delayed responses as below for a discrete time signal

$$ x(n) = \sum_{k=-\infty}^{k=\infty} x(k)\delta(n - k)$$

Let the impulse response to this $\delta(n)$ input be $h(n)$ then the output is simply,

$$y(n) = \sum_{k=-\infty}^{k=\infty} x(k)h(n-k)$$

This is possible both because the system is linear as well as time invariant, so if the impulse response $\delta(n)$ is $ h(n)$ then the response for $\delta(n-k)$ is $h(n-k)$