**Unit 4: Sound and Music**

**Problem Set A**

**Overview:**

Problem Set A targets your ability to basic mathematical principles associated with the speed of sound and the intensity level of sound. The first five of the 15 problems pertain to the speed of sound. The last 10 of the 15 problems pertain to the intensity level of sound.

**Speed of Sound**

The speed of sound, like the speed of any wave, is dependent upon
the properties of the medium through which it is moving. For a sound
wave moving through air, the primary property of air which effects
its speed is the temperature of the air. There are a couple of
equations which describe the speed
(**v**) - temperature
(**T**) relationship; the following
might be the easiest to remember:

where **T** is the Celsius
temperature of the air through which the sound wave is moving. At 0
degrees Celsius, the speed of sound is 331 m/s. For every degree
Celsius above 0, the speed of sound increases by approximately 0.6
m/s. This equation provides a rather accurate estimate of the speed
of sound for temperatures upwards towards 50 degrees Celsius.

The speed of a wave (**v**) is
defined as the distance traveled
(**d**) per time of travel
(**t**) and is described by the
following equation:

Thus, the distance traveled by a wave is related to the time required for it to travel that distance. Problems #4 and #5 of this set will target your understanding of this relationship.

**Intensity Level of Sound**

Sound waves are produced by a vibrating object - vocal chords,
guitar string, or diaphragm on a speaker. The sound waves begin at a
point (or approximately a point) and then propagate through space in
three dimensions. As the sound wave propagates, it creates a wave
front that fills the surface area of an ever-expanding sphere. A
sound wave (like any wave) is often referred to as an
energy-transport phenomenon. The rate at which energy is put into the
wave is referred to as the **power of the
source**. Power (**P**) is
expressed in units of Watts. As these vibrations propagate through
space, they become less intense as the size of the spherical wave
front expands. Whatever energy is created by the wave at the source
fills the surface area of a sphere some distance
**R** away. Because the sphere is
constantly expanding, the energy is becoming *diluted* with
increasing distance from the source. The
**sound intensity**
(**I**) at any given location is
defined as the rate at which energy passes through that location.
Because the wave is filling a surface area, intensity is often
expressed in units of Watts/meter^{2} and given by the
equation

The human ear is sensitive enough to detect the smallest of
vibrations. The lowest amplitude vibration which most humans can hear
is defined as the **threshold of
hearing** (TOH). While such a sound will be different for
different people, the intensity associated with this sound is defined
as **1.0 x 10 ^{-12}
W/m^{2}**. The range of sound intensities which a
typical human can detect is enormous. sound which 100 billion times
more intense than the threshold of hearing (1 x 10

Often times, the sound level in decibels is known and the the
intensity in W/m^{2} is desired. In such instances the
related equation below can be used.

**Additional Readings/Study
Aids:**

The following pages from The Physics Classroom tutorial may serve to be useful in assisting you in the understanding of speed of sound waves and the intensity of sound waves.

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