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# Introduction

#### Sound Waves and Pressure: Introduction

The source of all sound is vibrating matter whether the matter is a gas, liquid, or solid. Vibrations in matter consist of what are termed standing waves within the matter. The best example of a standing wave is a guitar string after it has been plucked. The most obvious standing wave in the string is the wave that has a maximum displacement in the center of the string and zero displacement at its ends where it is attached to the guitar neck and the body.

The string is in constant, non-random motion. The motion of the standing wave is invariant and repeated so rapidly that the wave appears to be “standing” still. The full motion of the string occurs in the center and is termed an antinode. The ends where the string does not move are termed nodes. At least two additional standing waves occur in a guitar string and most vibrating matter. These standing waves have two and three antinodes that result in overtones or harmonics.

As previously stated, liquids and gases can vibrate and in so doing standing waves are created. The air inside a pipe of a pipe organ is caused to vibrate in a standing wave when pressurized air is forced into the pipe. The standing wave would appear as in Figure 1, except that the gas molecules of the air, not the guitar string would be moving back and forth in the standing wave.

The vibration of a standing wave causes surrounding matter to be displaced in waves that move away from the standing wave. These longitudinal waves take the form of pressure waves since the vibration of a standing wave alternately causes surrounding matter to be compressed and expanded. Again, this is most easily understood using the example of a guitar string. The standing wave of the vibrating string alternately compresses the gas molecules in the surrounding air and allows the molecules to expand. Every time the antinode of the standing wave is at its greatest deflection at the top of its motion, the molecules on that side of the string are compressed into a smaller volume. Every time the antinode is at its greatest opposite deflection at the bottom of its motion, the molecules on that side of the string are allowed to expand into a larger volume.

The longitudinal pressure wave propagates itself as molecules in the air surrounding the initial pressure wave are subjected to the same alternating compression and expansion. In this way, the initial vibration that caused the standing wave can be transferred from the original vibrating matter to any surrounding air or any other matter that the pressure wave contacts.

We detect sound due to the pressure waves that eventually make their way from a vibrating object like a guitar string to our ears. The alternating regions of compression and expansion in the air cause the eardrum in each ear to vibrate effectively transferring the vibrations of the string to our eardrums. The vibrations in our eardrums take the form of a standing wave. The vibrations of our eardrums are transferred to small bones in our middle ear causing them to move back and forth with the same motion as the standing wave. The motion of the small bones is then transferred to the inner ear. The inner ear contains approximately 30,000 stereocilia or “hair cells” which respond to the vibrations by sending neural impulses to the brain.

Two characteristics define both the standing wave in a vibrating object and the pressure waves that it generates. One is the frequency which is defined as the number of vibrations that occur in one second or, as in the case of a pressure wave, the number of compressions or expansions that pass a fixed point every second. The unit of frequency is the Hertz which has the units of 1/second. The human ear can detect sounds between 20Hz and 20,000Hz. We detect pressure waves with low frequencies as having a low pitch and pressure waves with high frequencies as having a high pitch. Pitch is really a musical term that describes our perception of the frequency.

The second characteristic is the wavelength. In the case of standing waves, it is the distance in meters between successive nodes that bracket the two opposing antinodes. In the case of a pressure wave, it is the distance between two successive expansions or compressions.

When considering the speed of a pressure wave, both the frequency and the wavelength of the wave must be considered. The frequency and the wavelength of a pressure wave are related to one another by the speed according to the following equation:

The speed of a pressure wave has units of meters/second. If the units for all three properties of a wave are substituted into the equation, the relationship among them is more easily observed:

Within the same type of matter, the speed of sound is constant. Given that the speed is a constant, the wavelength and frequency are related by an inverse relationship. As the frequency of sound increases, the wavelength must decrease. As the frequency of sound decreases, the wavelength must increase. Consider a sound with a high frequency and a sound with a low frequency. In the same type of matter, air, for example, the first sound would have a shorter wavelength than the second.

For example, the speed of sound in air is approximately 330 m/sec. A sound with a frequency of 33 Hz, just above the threshold of human hearing would have a wavelength of 10 meters. A sound with a frequency of 330 Hz, a frequency within the C scale, would have a wavelength of 1 meter.

Since pressure waves alternately cause a compression and expansion of matter, the speed of a pressure wave is dependent on the type of matter through which it travels. A greater attraction between the atoms or molecules found in the matter, the faster the speed of a sound wave that is traveling through it. Typically, the speed of sound is greater in solids, less in liquids, and least in gases due to a greater degree of attractive forces in solids compared to liquids and compared to gases.

#### GET FOCUSED

The Focus Questions in each Investigation are designed to help teachers and students focus on the important concepts. By the end of the CELL, students should be able to answer the following questions:

##### Investigation 1:
• How are sounds produced?
• How is sound transferred from one object or substance to another?
• What is the relationship between the wavelength and frequency of a standing wave and the sound it produces?

##### Investigation 2:
• What is the speed of sound in air?
• In the same type of matter, is the speed of sound different for different frequencies and wavelengths?
• What is the relationship between the wavelength and frequency of a standing wave and the sound it produces?

##### Investigation 3:
• How do different types of matter affect the speed, the wavelength, and the frequency of sound?

# CONTENT

• Fun Facts
• Learn the Lingo
• Get Focused

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## Vibrations

All of the sounds that we hear (and even those we can’t hear) are caused by vibrations. When an object vibrates it affects the air molecules around it by causing them to vibrate at the same frequency. Frequency is simply a measure of the vibrations that occur over a set period of time – one second, for example.

Musical instruments generate their unique sounds through vibrations of various types. The drum skin vibrates when struck with the hand or drumstick. Guitars, violins, and other string instruments make sounds with vibrating strings, as do pianos when their string are struck with hammers attached to the keys.

Even the human voice creates sound waves through vibrations. Just place your hand on your throat when you talk or sing and you will easily feel your vocal cords vibrating.

## Heinrich Hertz: Frequency

Heinrich Hertz was a German scientist who’s short life lasted from 1857 to 1894. In honor of the accomplishments the international unit of frequency was named after him (the Hertz). For our purposes, a Hertz is the number of cycles per second of a sound wave. The figure below depicts a 1 Hertz and a 7 Hertz sound wave. Notice how the 7 Hertz wave has 7 cycles in the 1 second shown on the graph.

Below is a table showing the seven notes of the musical scale around the piano middle C (~262 Hz).

Finally, the LabLearner video below will permit you to hear sound waves of 1,000 Hz, 262 Hz (middle C), 125 Hz, and 62.5 Hz. When you play the video, notice how the lower the frequency (Hertz, Hz) the lower the tone of the sound.

#### LEARN THE LABLEARNER LINGO

The following list includes Key Terms that are introduced within the Backgrounds of the CELL. These terms should be used, as appropriate, by teachers and students during everyday classroom discourse.

Note: Additional words may be bolded within the Background(s). These words are not Key Terms and are strictly emphasized for exposure at this time.

##### Investigation 1:
• Vibration: The repeated back and forth movement of an object or substance
• Standing wave: A wave that forms in a vibrating object. A standing wave does not move through space, it forms due to repeated vibrations of the object.
• Node: The point at which a standing wave has no displacement and therefore does not move back and forth
• Antinode: The point at which a standing wave has its maximum displacement back and forth
• Pressure wave: The moving wave that is produced by a standing wave. The back and forth movement of a standing wave’s vibrations cause the compression and expansion of a pressure wave that travels away.
• Frequency: The number of times an object vibrates every second and the number of times a standing wave moves back and forth every second.
• Wavelength: The length in meters of a complete standing wave from the node that defines where it begins to the node that defines where it ends. The units are meters.
• Pitch: Frequency is related to how we perceive sounds. We perceive sounds with a high frequency as having a high pitch and sounds with a low frequency as having a low pitch.
##### Investigation 2:
• Speed: How fast anything, in this case, the pressure waves of a sound, travels. The units are meters per second.
• Hertz: The unit of frequency in 1/second
##### Investigation 3:
• There are no new Key Terms introduced in Investigation 3.