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Lesson 3.3
Lesson 3.1 |
Lesson 3.3 Resonance Overview This lesson deals with natural frequencies and resonance. On completion of this lesson you should be able to use the pendulum formula to determine the natural frequency of a simple pendulum. You should also be able to explain why large forces can sometimes result from the accumulation of a series of relatively small regular pulses. MINI LAB
CHOICE OF ACTIVITIES
Natural Frequencies When struck briefly, most objects will emit a sound with a characteristic frequency pattern. Generally, the shape and material of the object permits standing waves to persist in the object for a short period. Some objects such as bells and springs allow the vibrations to persist for longer periods but in all cases there is a frequency or combination of frequencies that is dominant. These are the natural frequencies of the objects. Oscillating objects lose energy – generally due to friction. Additional energy must be provided if continuous oscillation needs to be maintained. The amount of energy needed to sustain oscillation at the natural frequency is considerably less that would be needed to produce continuous oscillation at a different frequency. Pendulums, swings and springs, for example, have definite natural frequencies and require considerable energy to cause them to oscillate at any other frequency. Natural frequencies and beat frequencies need to be taken into account when designing structures and equipment that could be subject to vibration. Waves The crests and troughs of waves are the points at which maximum displacement of the medium occur. These terms generally apply to transverse waves although longitudinal waves will have points at which maximum and minimum compressions occur. Crests are sometimes referred to as peaks. A sign convention is used in which crests represent maximum positive displacement and troughs represent maximum negative displacement. In a wave traveling along the surface of a liquid, positive displacement would be upwards and negative displacement downwards. If crests and troughs are referred to in a horizontally oscillating waves (e.g. an oscillating string or rope), it will need to be decided as to whether movement to the left or right should be assigned a positive value. Wave Velocity Wave velocity is the distance moved by a wave per second. Frequency Frequency of a wave is the number of oscillations per second. This is also the number of wavelengths covered per second by the movement of the wave. The unit of frequency is the Hertz (Hz) where 1 Hz = 1 oscillation per second (Or 1 cycle per second) Period The period of a wave is the time taken for one complete oscillation or cycle. It is the time taken for one wavelength to pass a given point. The period is the inverse of the frequency: P = 1/f Amplitude The amplitude of a wave refers to the maximum displacement of the medium during an oscillation. It is numerically equal to the size of the crest. Attenuation occurs when damping of the wave occurs to reduce the amplitude. Wave intensity is a measurement of the energy carried by a wave. It depends on the amplitude and frequency of the wave. Wave-front A wave-front is a line or section taken through a 3-dimensional wave which joins all points that are in the same position or state in their oscillations. Wave-fronts are at right angles to the direction of the waves and can have a variety of shapes. For example, wave-fronts can be straight lines, circular, spherical or planar.
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