Kristela Milan

III - Galileo

INTRODUCING SOUND WAVES

Sound surrounds us all the time. From the chirping of birds when we wake up to the croaking of frogs at night. All the sounds that we hear have one thing in common. Every sound is produced by vibrations of an object. When an object vibrates, it makes the surrounding air vibrate. The vibrations in the air travel outward in all directions from the object. When the vibrations enter our ears, the brain interprets them as sounds. Although many of the sounds we hear travel through the air, sound can move through any material. Acoustics is the science of sound and of its effects on people.

SOUND

If you drop a pebble into a still pond, you will see a series of waves that travel outward from the point where the pebble struck the surface. Sound also travels in waves as it moves through the air or some other medium (substance). The waves are produced by a vibrating object.

THE NATURE OF SOUND

As a vibrating object moves outward, it compresses the surrounding medium producing a region of compression called condensation. As the vibrating object then moves inward, the medium expands into the space formerly occupied by the object. This region of expansion is called rarefaction. Sound waves consist of these condensations and rarefactions.

Sound waves must travel through a medium. Thus, sound is absent in outer space, which contains no material for a vibrating object to compress and expand.

Sound is a longitudinal wave because the vibrations are in the same direction as the motion and speed of the wave. This is most easily pictured if you imagine a slinky stretched slightly across a tabletop.

LONGITUDINAL WAVE

Sound is created by the alternating compression and expansion of air. Sound travels at a speed of 331 m/s at 0°C. The speed increases as the temperature of the air increases, at a rate of 0.6 m/s per Celsius degree. If something moves faster than sound, it is said to be supersonic. If it travels at the speed of sound, it travels, Mach 1; three times the speed of sound is called Mach 3.

Frequency of sound waves refers to the number of condensations or rarefactions produced by a vibrating object each second.

Pitch is the degree of highness or lowness of a sound as perceived by a listener.

FREQUENCY AND PITCH

The more rapidly an object vibrates, the higher will be the frequency. Scientists use a unit called hertz to measure frequency. One hertz equals one cycle (vibration) per second. As the frequency of sound waves increases, the wavelength decreases.

FREQUENCY

A higher-frequency sound has a higher pitch. Frequencies of sound waves that humans can hear range from about 20-20,000 hertz or cycles per second. The loudness of the sound is related to the wave’s energy or intensity.

1. Wavelength is the distance between any point on one wave and the corresponding point on the next one.

2. Infrasound is the sound with frequencies below the range of human hearing which is 20-20,000 hertz.

3. Ultrasound is the sound with frequencies above the range of human hearing which is 20-20,000 hertz.

4. Resonance Frequency is approximately the frequency at which an object would vibrate naturally if disturbed in some way.

TERMS TO REMEMBER IN FREQUENCY

High-pitched sounds have higher frequencies than low-pitched sounds. Musical instruments can produce a wide range of pitches. For example a trumpet has valves that can shorten or lengthen the vibrating column of air inside the instrument. A short column produces a high-frequency, high-pitched sound. A long column results in a note of low-frequency and low-pitch.

PITCH

Intensity of a sound is related to the amount of energy flowing in the sound waves. Intensity depends on the amplitude of the vibrations producing the waves. Amplitude is the distance that a vibrating object moves from its position of rest as it vibrates. The larger the amplitude of vibration is, the more intense will be the sound. Decibel is the unit used to measure the intensity level of a sound. A 3,000 hertz tone of zero decibels is the weakest sound that the normal human ear can hear.

INTENSITY AND LOUDNESS

The loudness of a sound refers to how strong the sound seems to us when it strikes our ears. A high-frequency or low-frequency sound does not seem as loud as a sound of the same intensity in the middle of the frequency range because our ears have low sensitivity to sounds near the upper and lower limits of the range of frequencies that we can hear.

Take note: The loudness of a sound decreases as the distance increases between a person and the source of the sound.

Sound Quality, also called timbre, is a characteristic of musical sounds. Quality distinguishes between sounds of the same frequency and intensity produced by different musical instruments.

Almost every musical sound consists of a combination of the actual note sounded and a number of higher tones related to it. The actual note played is the fundamental. The higher tones are overtones. The number and strength of the overtones help determine the characteristic sound quality of a musical instrument.

Loudness and intensity can be confusing because loudness is a measurement based on the sensation caused in a human by sound intensity. Because the human ear is sensitive over a very large range of intensity, loudness is defined using a logarithmic scale. A sound wave that is twice as loud has roughly ten times the intensity.

LOUDNESS AND INTENSITY

β (in dB) = 10 log ( I /Io) (Eqn. 12.1)

Where:

β – is the loudness measured in decibels (dB)

I – is the intensity of the sound wave in watt/m²

Io – is the constant equal to 1 x watt/m²

- represents the most faintly heard sound by humans and is defined as the loudness

of 0 dB.

Scientists use a unit called the decibel to measure the intensity level of a sound. A 3,000 hertz of zero decibels marks the threshold of audibility – the weakest sound that the normal ear can hear. A sound intensity level of 140 decibels is the threshold of pain. A whisper amounts to about 20 decibels. Ordinary conversation has an intensity level of about 60 decibels. Loud rock music can produce up to 120 decibels.

The sound in a particular place has an intensity of 2.0 x W/m². What is the loudness of that sound? If the intensity is tripled, what is its corresponding loudness?

Given:

Sound intensity I 2.0 x W/m²

EXAMPLE

Find:

A. Loudness (β) at the current intensity B. Loudness (β) if the current is tripled

Solution:A. Loudness (β) at the current intensity

β (in dB) = 10 log ( I /Io)

= 10 log ()= 10 log (2.0 x )= 10 (5.3) = 53 dB

B. Loudness (β) if the current is tripled

Sound Intensity = 3 (2.0 x W/m²)

= 6.0 x W/m²

β (in dB) = 10 log ( I /Io)

= 10 log ()= 10 log (6.0 x )= 10 (5.8) = 58 dB

Phon is a unit often used to measure the loudness level of tones. The loudness level in phons of any tone is the intensity level in decibels of a 1,000 hertz tone that seems equally loud.

The speed of sound depends on the medium through which the sound waves travel. The properties of a medium that determine the speed of sound are density and compressibility.

SPEED OF SOUND

DENSITY is the amount of material in a unit volume of a substance.

COMPRESSIBILITY measures how easily a substance can be crushed into smaller volume.

Note: The denser a medium is and the more compressible it is, the slower the speed of the sound is.

In general, liquids and solids are denser than air. But they are also far less compressible. Therefore, sound travels faster through liquids and solids than it does through air. Compared with its speed through air, sound travels about 4 times faster through water and about 15 times faster through steel. The speed of sound through air is commonly measured at sea level at 59F. The speed of sound, which is 340 m/s increases as the air temperature rises.

Jet airplanes sometimes fly at supersonic speeds. A plane flying faster than the speed of sound creates shockwaves, strong pressure disturbances that build up around the aircraft. People on the ground hear a loud noise, known as a sonic boom, when the shock waves from the plane sweep over them.

Table 12.1 Speed of Sound in various media

Medium Speed in ft/s Speed in m/s

Air at 59 F 1,116 340

Aluminum 16,000 5,000

Brick 11,980 3,650

Distilled Water at 77°F

4,908 1,496

Glass 14,900 4,540

Seawater at 77°F

5,023 1,531

Steel 17,100 5,200

Wood (sample) 13,480 4,110

The speed of sound v is related to the frequency f and wavelength λ of the sound wave by the following formula:

v = f λ (Eqn. 12.2)

You could also assume sound to be traveling constant across a medium, thus you can apply the following velocity equation:

d = vt (Eqn. 12.3)

Where d is the distance of the sound heard, t is the time before you heard the sound and v is the speed of sound.

Example 12.2 Gunshot heard

Using binoculars, you saw someone fired a gun from a distance. You heard the sound 2 seconds later. How far away are you from the person? Use the speed of sound 340 m/s.

Given:

time before sound is heard (t) 2 s

Find: Distance from the person who fired the gun (d)

Solution:

Using Eqn. 12.3, d = vt = 340 m/s (2 s) = 680 meters away.