The Components of Sound

Use of the dB in Sound Measurements

Sound intensity is defined as the sound power per unit area perpendicular to the wave. Units are typically in watts/m² or watts/cm². For sound intensity, the dB equation becomes:

$$\Delta I(db)=10log\frac{I_{2}}{I_{1}}$$

However, the power or intensity of sound is generally not measured directly. Since sound consists of pressure waves, one of the easiest ways to quantify sound is to measure variations in pressure (i.e. the amplitude of the pressure wave). When making ultrasound measurements, a transducer is used, which is basically a small microphone. Transducers like most other microphones produced a voltage that is approximately proportionally to the sound pressure (P). The power carried by a traveling wave is proportional to the square of the amplitude. Therefore, the equation used to quantify a difference in sound intensity based on a measured difference in sound pressure becomes:

$$\Delta I(db)=10log\frac{I_{2}}{I_{1}}=10log\frac{P^{2}_{2}}{P^{2}_{1}}=20log\frac{P_{2}}{P_{1}}$$

(The factor of 2 is added to the equation because the logarithm of the square of a quantity is equal to 2 times the logarithm of the quantity.) Since transducers and microphones produce a voltage that is proportional to the sound pressure, the equation could also be written as:

$$\Delta I(db)=20log\frac{V_{2}}{V_{1}}$$

where: delta I is the change in sound intensity incident on the transducer and V₁ and V₂ are two different transducer output voltages. Revising the table to reflect the relationship between the ratio of the measured sound pressure and the change in intensity expressed in dB produces:

Ratio between Measurement 1 and 2	Equation	dB
1/2	dB = 20 log (1/2)	- 6 dB
1	dB = 20 log (1)	0 dB
2	dB = 20 log (2)	6 dB
10	dB = 20 log (10)	20 dB
100	dB = 20 log (100)	40 dB
1,000	dB = 20 log (1000)	60 dB
10,000	dB = 20 log (10000)	80 dB
100,000	dB = 20 log (100000)	100 dB
1,000,000	dB = 20 log (1000000)	120 dB
10,000,000	dB = 20 log (10000000)	140 dB
100,000,000	dB = 20 log (100000000)	160 dB
1,000,000,000	dB = 20 log (1000000000)	180 dB

From the table it can be seen that 6 dB equates to a doubling of the sound pressure. Alternately, reducing the sound pressure by 2, results in a – 6 dB change in intensity.

Pitch

Pitch helps us distinguish between low and high sounds. Imagine that a singer sings the same note twice, one an octave above the other. You can hear a difference between these two sounds. That is because their pitch is different.

Pitch depends on the frequency of a sound wave. Frequency is the number of wavelengths that fit into one unit of time. Remember that a wavelength is equal to one compression and one rarefaction. Even though the singer sang the same note, because the sounds had different frequencies, we heard them as different. Frequencies are measured in hertz. One hertz is equal to one cycle of compression and rarefaction per second. High sounds have high frequencies and low sounds have low frequencies. Thunder has a frequency of only 50 hertz, while a whistle can have a frequency of 1,000 hertz.

The human ear is able to hear frequencies of 20 to 20,000 hertz. Some animals can hear sounds at even higher frequencies. The reason we cannot hear dog whistles, while they can, is because the frequency of the whistle is too high be processed by our ears. Sounds that are too high for us to hear are called ultrasonic.

Ultrasonic waves have many uses. In nature, bats emit ultrasonic waves and listen to the echoes to help them know where walls are or to find prey. Captains of submarines and other boats use special machines that send out and receive ultrasonic waves. These waves help them guide their boats through the water and warn them when another boat is near.

Tone & Harmonics

Another difference you may have noticed between sounds is that some sounds are pleasant while others are unpleasant. A beginning violin player sounds very different than a violin player in a symphony, even if they are playing the same note. A violin also sounds different than a flute playing the same pitch. This is because they have a different tone, or sound quality. When a source vibrates, it actually vibrates with many frequencies at the same time. Each of those frequencies produces a wave. Sound quality depends on the combination of different frequencies of sound waves.

Imagine a guitar string tightly stretched. If we strum it, the energy from our finger is transferred to the string, causing it to vibrate. When the whole string vibrates, we hear the lowest pitch. This pitch is called the fundamental. Remember, the fundamental is really only one of many pitches that the string is producing. Parts of the string vibrating at frequencies higher than the fundamental are called overtones, while those vibrating in whole number multiples of the fundamental are called harmonics. A frequency of two times the fundamental will sound one octave higher and is called the second harmonic. A frequency four times the fundamental will sound two octaves higher and is called the fourth harmonic. Because the fundamental is one times itself, it is also called the first harmonic.

How is this knowledge useful in everyday life?

The more harmonics a sound has, the fuller the quality the sound is. All the different overtones of a sound help give it a unique pattern. This is especially true for a person’s voice. Everybody in the world has a different voice print, or pattern of overtones. Detectives can track a criminal if they know his voice print just as they would use his fingerprints. Voice identification equipment is used in advanced security systems to recognize and let in only one authorized person. Voice prints are also used in modern technology, for example, voice activated telephones. In the future, if you want the lights on, it may be more common to say, “Turn on lights,” than to flip a light switch.

What is the difference between music and noise?

Both music and noise are sounds, but how can we tell the difference? Some sounds, like construction work, are unpleasant. While others, such as your favorite band, are enjoyable to listen to. If this was the only way to tell the difference between noise and music, everyone’s opinion would be different. The sound of rain might be pleasant music to you, while the sound of your little brother practicing piano might be an unpleasant noise. To help classify sounds, there are three properties which a sound must have to be musical.

A sound must have an identifiable pitch, a good or pleasing quality of tone, and repeating pattern or rhythm to be music. Noise on the other hand has no identifiable pitch, no pleasing tone, and no steady rhythm.