No, the emitter of a sound wave does not experience an opposite and equal reaction in terms of direction. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. However, this law applies to the overall forces experienced by objects, not specifically to the direction of a sound wave.
When a sound wave is produced by an object, the sound wave propagates outward in all directions from the source. The sound wave itself carries energy and information, but it does not exert a significant mechanical force on the source of the sound. Therefore, there is no direct opposite and equal reaction in terms of the direction of the sound wave.
For example, if you clap your hands, the sound waves generated spread out in all directions from your hands. While your hands experience a force upon contact during the clapping motion, the subsequent sound waves do not exert a significant force back on your hands.
It's important to note that the transmission of sound waves involves the transfer of energy, and that energy comes from the object creating the sound. However, the reaction force associated with sound waves is not typically a significant factor in terms of the object's motion or movement.