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14 Wave speed

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Introduction Waves are one way in which energy is transferred from place to place.How quickly they do this depends on their speed, which may be anything up to c, the speed of light, 3 x 108 m s-1

Speed, frequency and wavelengthThe waves considered so far are described as progressive waves.They travel through space.The speed, v of the wave indicates how fast it movesThe speed is the distance travelled per second by a crest.The opposite of a progressive wave is a standing wave.

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Speed, frequency and wavelength

Speed v is related to frequency f and wavelength λ by:

speed = frequency x wavelength v = fλ

If a train of f waves, each of length λ, pass a point in 1 s, the total length of the train is fλ.This is the length of the waves passing per second i.e. the speed of the wave.A note on units frequency f is in hertz (Hz)Wavelength λ is in metres (m)Since 1 Hz = 1 s-1, multiplying f x λ gives a result in m Hz, or m s-1. This is the correct unit for speed.

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Worked example1. An observer, standing at the end of a pier, observes one wave

passing by every 8 s. the distance between adjacent waves is 12 m. calculate the speed of the waves.

SolutionStep 1 calculate the frequency of the waves.

f = 1 / T = 1 / 8 s = 0.125 HzStep 2 Note down the wavelength of the waves

λ = 12 mStep 3 calculate the wave speed

speed v = fλ = 0.125 Hz x 12 m = 1.5 m s-1.2. Calculate the wavelength of an electromagnetic wave (speed =

3 x 108 m s-1) of frequency 100 GHz.Solution Step 1 Write down the quantities; convert to scientific notation (powers of 10): v = 3 x 108 m s-1 , f = 100 x 109 Hz, λ = ?Step 1 rearrange the wave equation, substitute the values and solve

λ = v / f = 3 x 108 m s-1 / 100 x 109 Hz = 3 x 10-3 m

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Questions

1. Calculate the speed of ripples whose wavelength is 3 mm and whose frequency is 15 Hz.

2. Calculate the frequency of a sound wave if its wavelength in air is 11 mm (speed of sound in air = 330 ms-1)