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**Properties of Mechanical Waves**

Frequency, Period, Wavelength, Amplitude and Wave Speed (yes another formula!)

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Period The period of a pendulum is the time it takes to move through one cycle This is from when the string is pulled to one side, let go and the ball moves to the opposite side and then returns to the starting place

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**Frequency Frequency is the number of complete cycles in a given time**

For a wave, the frequency is the number of wave cycles that pass a point in a given time Frequency is measured in cycles per second or hertz (Hz) A wave’s frequency equals the frequency of the vibrating source producing the wave

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**Equations for frequency and period**

T = 1/f or f = 1/T In the above equations: T stands for the period in time (seconds) and f stands for frequency in hertz If given the period of an object you can calculate the frequency Also if given the frequency of an object you can calculate the period

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Wavelength Wavelength is the distance between a point on one wave and the same point on the next cycle of the wave For a transverse wave, wavelength is measured between crests or troughs For longitudinal waves, the wavelength is measured between compressions or rarefractions

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**Wave Speed Vw = ƒ λ Vw = wave velocity (speed) ƒ = frequency**

λ = wavelength Wavelength is in meters (m) Frequency is in hertz (Hz) Wave velocity (speed) is in meters/second (m/s)

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Wave Speed Example One end of a rope is vibrated to produce a wave with a wavelength of 0.25 meters. The frequency of the wave is 3.0 hertz. What is the velocity of the wave? Vw = ƒ λ Wavelength (λ ) = 0.25 meters Frequency (ƒ) = 3.0Hz Vw= 0.25 meters x 3.0 Hz = 0.75m/s

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Wave Speed cont. The speed of a wave can change if it enters a new medium or if pressure or temperature change Most of the time, wave speed is constant If a wave is moving at a constant speed then the wavelength is inversely proportional to frequency waves with a lower frequency have a longer wavelength Waves with a higher frequency have shorter wavelengths

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Amplitude The amplitude of a wave is the maximum displacement of the medium from its rest position The more energy a wave has, the greater its amplitude

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