If standing waves are established in musical instruments like the guitar, then how do we hear the sound because standing waves don't transfer energy from one place to another. At least that's what I have learned.
My guess is that standing waves are established in the string itself but when the string vibrates, it also vibrates the air around it
The short answer is that the energy carried away as music is like a "loss" or "friction" term. It can be complicated though. For an electric guitar it arises from Lorentz forces with the pickups / coils. An acoustic guitar is very complicated, because the strings resonate with the sound hole. I have been interested in "rigorous physics of music" questions and it is hard to find analyses that aren't overly hand wavy.
As the comment above says, standing waves don't transfer energy across stationary nodes. Obviously, there are damped standing wave solutions with loss or friction terms that decay over time, and it is generally ignored but those loss terms never actually destroy energy.
