We extend the principle of optical index of refraction to apply the concept of acoustical index for transverse acoustical wave propagation in strings. The relationship between acoustical index and mass density of the acoustic material is developed. With this theoretical link established, classic index-matching techniques are explored at acoustical boundaries. Proper selection of boundary interface segments leads to the elimination of resonant vibrationalmodes that occur in rigidly supported strings, while maintaining the nonresonant vibration response.