Energy in Sound Waves, Forced Vibrations,Natural Frequency,Resonance

Energy in Sound Waves

Wave motion of all kinds possesses energy of varying degrees. Electromagnetic waves from the Sun, for instance, bring us the enormous quantities of energy that are necessary for life on Earth. By comparison, the energy in sound is extremely small. That's because producing sound requires only a small amount of energy. For example, 10,000,000 people talking at the same time would produce sound energy equal only to the energy needed to light a common flashlight. Hearing is possible only because of our remarkably sensitive ears. Only the most sensitive microphone can detect sound that is softer than what we can hear. 

Sound energy dissipates to thermal energy while sound travels in air. For waves of higher frequency, the sound energy is transformed into internal energy more rapidly than for waves of lower frequencies. As a result, sound of low frequencies will travel farther through air than sound of higher frequencies. That's why the foghorns of ships are of a low frequency.

Forced Vibrations

If we strike an unmounted tuning fork, the sound from it may be rather faint. If we hold the same fork against a table after striking it, the sound is louder. This is because the table is forced to vibrate, and, with its larger surface, the table will set more air in motion. The table will be forced into vibration by a fork of any frequency. This is a case of forced vibration.

The mechanism in a music box is mounted on a sounding board. Without the sounding board, the sound the music-box mechanism produces is barely audible. Sounding boards are important in all stringed musical instruments.

Natural Frequency

When someone drops a wrench on a concrete floor, we are not likely to mistake its sound for that of a baseball bat hitting the floor. This is because the two objects vibrate differently when they are struck. Tap a wrench and the vibrations it makes are different from the vibrations of a baseball bat, or of anything else. Any object composed of an elastic material when disturbed will vibrate at its own special set of frequencies, which together form its special sound. We speak of an object's natural frequency, which depends on such factors as the elasticity and shape of the object. Bells and tuning forks, of course, vibrate at their own characteristic frequencies. And, interestingly enough, most things from planets to atoms and almost everything else in between have a springiness to them and vibrate at one or more natural frequencies.

Resonance

When the frequency of forced vibrations on an object matches the object's natural frequency, a dramatic increase in amplitude occurs. This phenomenon is called resonance. Literally, resonance means "resounding," or "sounding again." Putty doesn't resonate because it isn't elastic, and a dropped handker- chief is too limp. In order for something to resonate, it needs a force to pull it back to its starting position and enough energy to keep it vibrating.

Reflection of Sound and Refraction of Sound

 Reflection of Sound

We call the reflection of sound an echo. The fraction of energy carried by the reflected sound wave is large if the surface is rigid and smooth and less if the surface is soft and irregular. Sound energy not carried by the reflected sound wave is carried by the "transmitted" (absorbed) wave.

Sound reflects from a smooth surface the same way that light does-the angle of incidence is equal to the angle of reflection (Figure 20.6). Sometimes, when sound reflects from the walls, ceiling, and floor of a room, the reflecting surfaces are too reflective and the sound becomes garbled. This is due to multiple reflections called reverberations. On the other hand, if the reflective surfaces are too absorbent, the sound level will be low and the hall will sound dull and lifeless. Reflection of sound in a room makes it sound lively and full, as you have probably discovered while singing in the shower. In the design of an auditorium or concert hall, a balance must be achieved between reverberation and absorption. The study of sound properties is called acoustics. 

It is often advantageous to place highly reflective surfaces behind the stage to direct sound out to an audience. Reflecting surfaces are suspended above the stage in some concert halls. The ones in Davies Hall in San Francisco are large shiny plastic surfaces that also reflect light (Figure 20.7). A listener can look up at these reflectors and see the reflected images of the members of the orchestra. The plastic reflectors are somewhat curved, which increases the field of view, Both sound and light obey the same law of reflection, so, if a reflector is oriented so that you can see a paricular musical instrument, rest assured that you will hear it also. Sound from the instrument will follow the line of sight to the reflector and than to you.

Refraction of Sound

Sound waves bend when parts of the wave fronts travel at different speeds. This happens in uneven winds or when sound is traveling through air of uneven temperatures. This bending of sound is called refraction. On a warm day, the air near the ground may be appreciably warmer than the rest of the air, so the speed of sound near the ground increases. Sound waves therefore tend to bend away from the ground, resulting in sound that does not seem to travel well. Different speeds of sound produce refraction.

We hear thunder when the lightning is reasonably close, but we often fail to hear the thunder for distant lightning because of refraction. The sound travels slower at higher altitudes and bends away from the ground. The opposite often occurs on a cold day or at night when the layer of air near the ground is colder than the air above. Then the speed of sound near the ground is reduced. The higher speed of the wave fronts above causes a bending of the sound toward the ground, resulting in sound that can be heard over considerably longer distances (Figure 20.8)

Sound, Origin of Sound, Media That Transmit Sound

 Sound

If a tree fell in the middle of a deep forest hundreds of kilometers away from any living being, would there be a sound? Different people will answer this question in different ways. "No," some will say, "sound is subjective and requires a listener. If there is no listener, there will be no sound." "Yes," others will say, "a sound is not something in a listener's head. A sound is an objective thing." Discussions like this one often are beyond agreement because the participants fail to realize that they are arguing not about the nature of sound but about the definition of the word. Either side is correct, depending on the definition taken, but investigation can proceed only when a definition has been agreed upon. Physicists, such as the two shown above, usually take the objective position and define sound as a form of energy that exists whether or not it is heard, and they go on from there to investigate its nature.

Origin of Sound

Most sounds are waves produced by the vibrations of material objects. In a piano, a violin, and a guitar, the sound is produced by the vibrating strings; in a saxophone, by a vibrating reed; in a flute, by a fluttering column of air at the mouthpiece. Your voice results from the vibration of your vocal chords.

In each of these cases, the original vibration stimulates the vibration of something larger or more massive, such as the sounding board of a stringed instrument, the air column within a reed or wind instrument, or the air in the throat and mouth of a singer. This vibrating material then sends a disturbance through the surrounding medium, usually air, in the form of longitudinal waves. Under ordinary conditions, the frequency of the vibrating source and the frequency of the sound waves produced are the same.

We describe our subjective impression about the frequency of sound by the word pitch. Frequency corresponds to pitch: A high-pitched sound from a piccolo has a high frequency of vibration, while a low-pitched sound from a foghorn has a low frequency of vibration. The ear of a young person can normally hear pitches corresponding to the range of frequencies between about 20 and 20,000 hertz. As we grow older, the limits of this human hearing range shrink, especially at the high-frequency end. Sound waves with frequencies below 20 hertz are infrasonic, and those with frequencies above 20,000 hertz are called ultrasonic. We cannot hear infrasonic and ultrasonic sound waves.

Media That Transmit Sound

Most sounds that we hear are transmitted through the air. However, any elastic substance-whether solid, liquid, gas, or plasma-can transmit sound. Elasticity is the ability of a material that has changed shape in response to an applied force to resume its initial shape once the distorting force is removed. Steel is an elastic substance. In contrast, putty is inelastic.¹ In elastic liquids and solids, the atoms are relatively close together, respond quickly to one another's motions, and transmit energy with little loss. Sound travels about four times faster in water than in air and about fifteen times faster in steel than in air.

Relative to solids and liquids, air is a poor conductor of sound. You can hear the sound of a distant train more clearly if your ear is placed against the rail. Similarly, a watch placed on a table beyond hearing distance can be heard if you place your ear to the table. Or click some rocks together under water while your ear is submerged. You'll hear the clicking sound very clearly. If you've ever been swimming in the presence of motorized boats, you probably noticed that you can hear the boats' motors much more clearly under water than above water. Liquids and crystalline solids are generally excellent conductors of sound-much better than air. The speed of sound is generally greater in solids than in liquids, and greater in liquids than in gases. Sound won't travel in a vacuum, because the transmission of sound requires a medium. If there is nothing to compress and expand, there can be no sound.