Reflectance of Sound Waves

Up to this point, my blog posts have focused on how sound is produced and how it is transmitted through air. Sound displays other behaviors, however, as it passes through air and comes into contact with other objects. Sound's behavior is very similar to that of light. When light comes in contact with an object, it can be transmitted, absorbed, or reflected. Every substance has an index of refraction, which dictates how it reflects and refracts light. This can be modeled by the following equation where R is reflectance and the n values are the indices of refraction:

(The Physics of Music and Color)

The index of refraction is a part of the relationship v=c/n where v is the wave velocity, c is the speed of light, and n is the index of refraction. With a known index of refraction, the wave velocity for different mediums can be calculated, and the above equation can be written in terms of wave velocity. This allows us to connect to the equation for sound reflectance, which must account for mass density(p) as well. The equation for the reflectance of sound is given by the following equation:

(The Physics of Music and Color)

In this equation, the P values represent the mass densities and the v values represent the wave velocity of sound. This allows us to calculate the percentage of sound that reflects off of a medium when we know the mass density of the medium and the wave velocity of sound. 

Knowing how much sound certain materials reflect has a nice application in the world of music. When constructing a music studio, you will want to have a space where you can monitor sound in an ideal setting. If sound reflects significantly off of the surfaces of your studio space, it becomes less than ideal for accurate mixing. The materials of the walls in a music studio should be made of a substance that reflects sound as little as possible. This is why you often see sponge-like material on the walls of treated rooms; they absorb sound and reflect a very low percentage of it. 

Works Cited:

1.  Gunther, Leon. The Physics of Music and Color. New York, New York: Springer, 2012.