What justifies is that people did it, and found that the reflected signal was at the same frequency, every time (almost). Science is, at the heart, an empirical process.
What we find is that the way sound operates and interacts with mediums is defined by a wave equation: $\frac{\partial^2u}{\partial t^2}=c^2\frac{\partial^2u}{\partial x^2} $ Whether you know calculus or not, its an equation which predicts the behavior of sound and other "waves" astonishingly well. So well, in fact, that we turn it around and say that anything which obeys that equation, for any reason, is a "wave".
Now if you have enough calculus and differential equations under your belt to explore this, you find that the time evolution operator for waves is linear -- the way they change over time is a "linear operator." One of the side effects of a linear operator is that they cannot change frequencies. If you have a frequency on the input, it may only be turned into the same frequency on the output. You need a non-linear operator to change frequencies.
But all of this is just math. The real reason is that we went out and analyzed a bunch of physical experiments, and found that sound waves always reflected at the same frequency. We worked all of the math on the back end, trying to make sense of the results we see. For example, when we notice that the frequency always comes back the same, that's a very strong indicator that the operator is probably linear, so we explored linear operators until we found one that worked! The why in science is almost always stemming from experiments. Very rarely does the why stem from the math, and when it does, we quickly work to identify experiments to back it up!
And note I've said almost. You can get some non-linearity here with a moving object. The effect is one we have heard many times in our life: a Doppler shift. Experimentally, we found that if you bounce a sound wave off of something that is moving it can change the frequency.
