This chapter explores the fundamental principles of vibration and wave motion, particularly in relation to sound and stringed musical instruments. It begins with an introduction to vibratory motion, emphasizing the distinction between matter transfer and wave propagation as mechanisms of energy transmission. A focus is placed on simple harmonic motion (SHM), its defining characteristics, and its mathematical representation in terms of displacement, velocity, and acceleration. The discussion then extends to wave propagation, differentiating between transverse and longitudinal waves, and highlighting their relevance to string vibrations and sound waves. The physics of standing waves, harmonic frequencies, and resonance are analyzed, particularly in the context of musical instruments. Through practical exercises and examples, the chapter provides insight into how tension, length, and mass density of a string influence its vibrational characteristics. The latter sections of the chapter explore the properties of sound, including its generation, propagation, and interaction with different media. The speed of sound, wave reflection, refraction, and interference patterns are examined to explain how sound behaves in various environments. Special attention is given to the role of the bridge in stringed instruments, detailing the forces exerted by vibrating strings and their effects on sound transmission. Finally, the chapter delves into the perceptual characteristics of sound—loudness, pitch, and timbre—exploring their physical underpinnings and psychological interpretations. The impact of the missing fundamental effect on auditory perception is discussed, providing insights into how different listeners may perceive the same sound differently. By bridging theoretical physics with practical applications in instrument making, this chapter serves as a foundational resource for luthiers and acoustic engineers seeking to optimize sound quality through precise control of vibrational behavior.