Acoustic Resonance

*sound science series # 6

Natural Frequency: The frequency at which an object vibrates when allowed to do so freely.

All objects vibrate when they are disturbed. When each object vibrates, it tends to vibrate at a particular frequency or set of frequencies. We call these frequencies an object's natural frequencies.

Example: a tuning fork will vibrate at only one frequency while a clarinet will vibrate at a set of frequencies.

Acoustic Resonance: Resonance involving sound waves

When objects or air particles vibrate, if the amplitude of the vibrations is large enough and if the frequency of the vibration is within the human hearing range, then the object will produce sound waves which are audible.

Example of acoustic resonance in air columns closed at one end;

*Our own voice (the vocal tract acts as an air column closed at one end with the open end near the lips.

*Music produced by blowing into plastic bottles filled with water.

*Music produced by a clarinet.

Resonance: The transfer of energy of vibration from one object to another having the same natural frequency.

Vibration: Repeated pattern of motion, also called a cycle.

Some musical instruments based on resonance phenomenon:

 instruments with vibrating strings (which would include guitar strings, violin strings, and piano strings), open-end air column instruments (which would include the brass instruments such as the trombone and woodwinds such as the flute and the recorder), and closed-end air column instruments (which would include some organ pipe and the bottles of a pop bottle orchestra). A fourth category - vibrating mechanical systems (which includes all the percussion instruments). These instrument categories may be unusual to some; they are based upon the commonalities among their standing wave patterns and the mathematical relationships between the frequencies that the instruments produce.

 If the frequency of the external force is equal to the natural frequency of the body (or to it's integral multiple), then the amplitude of the forced vibrations (or oscillations) of the body becomes quite large. This phenomenon is called resonance.

Thus, resonance is particular case of forced vibrations (or oscillations).

Examples:

a. Mechanical reonance.

   i. army passing over a bridge.

   b. sound resonance.

   i. resonance box

   ii. vibration of strings

   iii. dtermination of frequency

   iv. pouring of water in a vessel

   v. vibration of surrounding

   vi. resonator

b. Electromagnetic resonance

   i. radio

The Dark Side of Resonance,  
The Tacoma-Narrows Bridge 

Every powerful phenomenon in nature has its dark side and resonance is no exception. It's best experienced in moderation. Taken to an extreme, resonance causes things to break catastrophically. For example, when an opera singer with a very loud voice hits the right frequency she can cause a champagne glass to resonate and break. 

On the morning of November 7, 1940, the four month old Tacoma Narrows Bridge began to oscillate dangerously up and down. A reporter drove out on the bridge with his cocker spaniel in the car. The bridge was heaving so violently that he had to abandon his car and crawl back to safety on his hands and knees.

At about 11:00 the bridge tore itself apart and collapsed. It had been designed for winds of 120 mph and yet a wind of only 42 mph caused it to collapse. How could this happen? No one knows exactly why. However, the experts do agree that somehow the wind caused the bridge to resonate. It was a shocking calamity although the only loss of life was the cocker spaniel.

example of the forced vibration: say if the natural frequency of a glass cup is 497.955 Hz. Producing the same frequency from a guitar, vibrations (resonance), glass cup can be broken. So this 497.955 Hz is a 'Critical Frequency' of the glass bowl here in this example.

                                       Nikola Tesla (1856 - 1943) - Master of Resonanc

Nikola Tesla - Master of Resonance: Tesla was a genius who was obsessed with resonance. No discussion of resonance could be complete with out talking about Tesla.

 It was an innocent experiment. Tesla had attached a small vibrator to an iron column in his New York City laboratory and started it vibrating. At certain frequencies specific pieces of equipment in the room would jiggle. Change the frequency and the jiggle would move to another part of the room. Unfortunately, he hadn't accounted for the fact that the column ran downward into the foundation beneath the building. His vibrations were being transmitted all over Manhattan.

 

Sharp and flat resonance: Sharpness of resonance is, in a way, a measure of the rate of  fall of amplitude from it's maximum value at resonant frequency, on either side of it. The sharper the fall in amplitude, the sharper the resonance.

 Law of conservation of energy: In the case of a falling object, initial potential energy transformed into other forms of energy, i.e. into heat or sound

(or in other word, when sound is absorbed, it turns into heat).

 *Note: all pictures thankfully shared from various sources.