Sound

Sound is associated with sense of hearing, and, therefore, with the physiology of our ears and the psychology of our brain, which interprets the sensations  that reach our ears. The term sound also refers to the physical sensation that stimulate our ears; namely, longitudinal waves.

We can distinguish three aspects of any sounds. First, there must be a source for a sound; as with any wave, the source of a sound is a vibrating object. Second, the energy is transferred from the source in the form of longitudinal sound waves. And third, the sound is detected by an ear or by a microphone.

Characteristics of Sound             

We usually think of sound waves traveling in the air, for normally it is the vibrations of the air that force our eardrums to vibrate. But sound waves can also travel in other materials. Two stones struck together under water can be heard by a swimmer beneath the surface, for the vibrations are carried to the ear by the water. When you put your ear flat against the ground you can hear an approaching train or truck. In this case the ground does not actually touch your eardrum, but the longitudinal wave transmitted by the ground is called a sound wave just the same, for its vibrations cause the outer ear and the air within it to vibrate. Clearly, sound cannot travel in the absence of matter. For example, a bell ringing inside an evacuated jar cannot be heard, and sound cannot travel through the empty reaches of outer space.

Intensity of Sound : Decibels

Like pitch, loudness is a sensation in the consciousness of a human being. It too is related to a physically measurable quantity, the intensity of the wave. Intensity is defined as the energy transported by a wave per unit time across a unit are perpendicular to the energy flow. Intensity is proportional to the square of the wave amplitude. Intensity has units of power per unit area, or watts/ meter² (W/m²).

The human ear can detect sounds with an intensity as low as 10^-12 W/m² and as high as 1 W / m² (and even higher, although above this it is painful). This is an incredibly wide range of intensity, spanning a factor of 10¹² from lowest to highest. Presumably because of this wide range, what we perceive as loudness is not directly proportional to the intensity. To produce a sound that sounds about twice as loud requires a sound wave that has about 10 times the intensity. This is roughly valid at any sound level for frequencies near the middle of the audible range. For example, a sound wave of intensity 10^-2 W/m² sounds to an average human being like it is about twice as loud as one whose intensity is 10^-3 W/m² and four times as loud as 10^-4 W/m².

Energy Transport and the Amplitude of a Wave

As mentioned earlier, a wave is an energy transport phenomenon that transports energy along a medium without transporting matter. A pulse or a wave is introduced into a slinky when a person holds the first coil and gives it a back-and-forth motion. This creates a disturbance within the medium; this disturbance subsequently travels from coil to coil, transporting energy as it moves. The energy is imparted to the medium by the person as he/she does work upon the first coil to give it kinetic energy. This energy is transferred from coil to coil until it arrives at the end of the slinky. If you were holding the opposite end of the slinky, then you would feel the energy as it reaches your end. In fact, a high energy pulse would likely do some rather noticeable work upon your hand upon reaching the end of the medium; the last coil of the medium would displace you hand in the same direction of motion of the coil. For the same reasons, a high energy ocean wave can do considerable damage to the rocks and piers along the shoreline when it crashes upon it.

The amount of energy carried by a wave is related to the amplitude of the wave. A high energy wave is characterized by a high amplitude; a low energy wave is characterized by a low amplitude. As discussed earlier in Lesson 2, the amplitude of a wave refers to the maximum amount of displacement of a particle on the medium from its rest position. The logic underlying the energy-amplitude relationship is as follows: If a slinky is stretched out in a horizontal direction and a transverse pulse is introduced into the slinky, the first coil is given an initial amount of displacement. The displacement is due to the force applied by the person upon the coil to displace it a given amount from rest. The more energy that the person puts into the pulse, the more work that he/she will do upon the first coil. The more work that is done upon the first coil, the more displacement that is given to it. The more displacement that is given to the first coil, the more amplitude that it will have. So in the end, the amplitude of a transverse pulse is related to the energy which that pulse transports through the medium. Putting a lot of energy into a transverse pulse will not affect the wavelength, the frequency or the speed of the pulse. The energy imparted to a pulse will only affect the amplitude of that pulse.

         Figure 1. Source : www.physicsclassroom.com

Consider two identical slinkies into which a pulse is introduced. If the same amount of energy is introduced into each slinky, then each pulse will have the same amplitude. But what if the slinkies are different? What if one is made of zinc and the other is made of copper? Will the amplitudes now be the same or different? If a pulse is introduced into two different slinkies by imparting the same amount of energy, then the amplitudes of the pulses will not necessarily be the same. In a situation such as this, the actual amplitude assumed by the pulse is dependent upon two types of factors: an inertial factor and an elastic factor. Two different materials have different mass densities. The imparting of energy to the first coil of a slinky is done by the application of a force to this coil. More massive slinkies have a greater inertia and thus tend to resist the force; this increased resistance by the greater mass tends to cause a reduction in the amplitude of the pulse. Different materials also have differing degrees of springiness or elasticity. A more elastic medium will tend to offer less resistance to the force and allow a greater amplitude pulse to travel through it; being less rigid (and therefore more elastic), the same force causes a greater amplitude.

The energy transported by a wave is directly proportional to the square of the amplitude of the wave. This energy-amplitude relationship is sometimes expressed in the following manner.

This means that a doubling of the amplitude of a wave is indicative of a quadrupling of the energy transported by the wave. A tripling of the amplitude of a wave is indicative of a nine-fold increase in the amount of energy transported by the wave. And a quadrupling of the amplitude of a wave is indicative of a 16-fold increase in the amount of energy transported by the wave. The table at the right further expresses this energy-amplitude relationship. Observe that whenever the amplitude increased by a given factor, the energy value is increased by the same factor squared. For example, changing the amplitude from 1 unit to 2 units represents a 2-fold increase in the amplitude and is accompanied by a 4-fold (2²) increase in the energy; thus 2 units of energy becomes 4 times bigger - 8 units. As another example, changing the amplitude from 1 unit to 4 units represents a 4-fold increase in the amplitude and is accompanied by a 16-fold (4²) increase in the energy; thus 2 units of energy becomes 16 times bigger - 32 units.

Forced Vibration

Musical instruments and other objects are set into vibration at their natural frequency when a person hits, strikes, strums, plucks or somehow disturbs the object. For instance, a guitar string is strummed or plucked; a piano string is hit with a hammer when a pedal is played; and the tines of a tuning fork are hit with a rubber mallet. Whatever the case, a person or thing puts energy into the instrument by direct contact with it. This input of energy disturbs the particles and forces the object into vibrational motion - at its natural frequency.

If you were to take a guitar string and stretch it to a given length and a given tightness and have a friend pluck it, you would hear a noise; but the noise would not even be close in comparison to the loudness produced by an acoustic guitar. On the other hand, if the string is attached to the sound box of the guitar, the vibrating string is capable of forcing the sound box into vibrating at that same natural frequency. The sound box in turn forces air particles inside the box into vibrational motion at the same natural frequency as the string. The entire system (string, guitar, and enclosed air) begins vibrating and forces surrounding air particles into vibrational motion. The tendency of one object to force another adjoining or interconnected object into vibrational motion is referred to as a forced vibration. In the case of the guitar string mounted to the sound box, the fact that the surface area of the sound box is greater than the surface area of the string means that more surrounding air particles will be forced into vibration. This causes an increase in the amplitude and thus loudness of the sound

This same principle of a forced vibration is often demonstrated in a Physics classroom using a tuning fork. If the tuning fork is held in your hand and hit with a rubber mallet, a sound is produced as the tines of the tuning fork set surrounding air particles into vibrational motion. The sound produced by the tuning fork is barely audible to students in the back rows of the room. However, if the tuning fork is set upon the whiteboard panel or the glass panel of the overhead projector, the panel begins vibrating at the same natural frequency of the tuning fork. The tuning fork forces surrounding glass (or vinyl) particles into vibrational motion. The vibrating whiteboard or overhead projector panel in turn forces surrounding air particles into vibrational motion and the result is an increase in the amplitude and thus loudness of the sound. This principle of forced vibration explains why demonstration tuning forks are mounted on a sound box, why a commercial music box mechanism is mounted on a sounding board, why a guitar utilizes a sound box, and why a piano string is attached to a sounding board. A louder sound is always produced when an accompanying object of greater surface area is forced into vibration at the same natural frequency.

Another common classroom demonstration of resonance involves a plastic tube containing an air column. The length of the air column was adjusted by raising and lowering a reservoir of water (dyed red). The raising and lowering of the reservoir adjusts the height of water in the open-air tube, and thus adjusts the length of the air column inside the tube. As the length of the air column is decreased, the natural frequency of the air column is increased. (Again note the length-wavelength-frequency relationship that was discussed earlier.) While adjusting the height of the liquid in the tube, a vibrating tuning fork is held above the air column of the tube. When the natural frequency of the air column is tuned to the frequency of the vibrating tuning fork, resonance occurs and a loud sound results. Quite amazingly, the vibrating tuning fork forces air particles within the air column into vibrational motion. Once more in this resonance situation, the tuning fork and the air column share the same vibrational frequency.

In conclusion, resonance occurs when two interconnected objects share the same vibrational frequency. When one of the objects is vibrating, it forces the second object into vibrational motion. The result is a large vibration. And if a sound wave within the audible range of human hearing is produced, a loud sound is heard.

REFERENCES

Diana Puspita and Iip Rohima. 2009. Alam Sekitar IPA Terpadu : untuk SMP/ MTs Kelas VIII. Jakarta ; Pusat Perbukuan, Departemen Pendidikan Nasional.

Giancoli. 2005. Physics : Principle with Application Sixth Edition. New Jersey: Pearson Education, Inc.

               

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