Force Vibrations and Resonance Forced Vibrations When a

Force Vibrations and Resonance

Forced Vibrations • When a tuning fork is struck with a rubber hammer, it vibrates at its fundamental frequency together with some low-order harmonics. The fundamental has a natural frequency that depends upon the fork's length, thickness, and composition. When a key on a piano is struck, the piano string vibrates at its fundamental frequency and at harmonics of this frequency. The only forces that affect these natural rates of vibration are friction and gravitation.

• Suppose we strike a tuning fork and then press its stem to a table top. The tone becomes louder when the fork is in contact with the table because the fork forces the table top to vibrate with the same frequency. Since the table top has a much larger vibrating area than the fork, these forced vibrations produce a more intense sound.

• A vibrating violin string stretched tightly between two clamps does not produce a very intense sound. When the string is stretched across the bridge of a violin, however, the wood of the violin is forced to vibrate in response to the vibrations of the string; the intensity of the sound is increased by these forced vibrations. The sounding board of a piano acts in the same way to intensify the sounds produced by the vibrations of its strings.

Resonance • The two tuning forks in Figure below have the same frequency. They are mounted on sounding boxes that increase the intensity of the sound through forced vibrations. One end of each sounding box is open.

• Suppose we place these forks a short distance apart, with the open ends of the boxes toward each other. Now let us strike one fork and, after it has vibrated several seconds, touch its prongs to stop them. • We find that the other fork is vibrating weakly. The compressions and rarefactions produced in the air by the first tuning fork act on the second fork in a regular fashion, causing it to vibrate. • Such action is called resonance, or sympathetic vibration. A person who screams into a piano with the damper pedal depressed may cause the piano strings that produce similar frequencies to vibrate.

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