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Lecture 6 - Mech. Waves (Ch. 13.7-13.8)

# Lecture 6 - Mech. Waves (Ch. 13.7-13.8) - Lecture 6(Ch 13...

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Lecture 6 (Ch 13): Mechanical Waves

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Sound as Pressure Waves Sound wave in air: The air “piles up” in areas of maximum pressure. This disturbance propagates as a wave as particles bump into each other.
Amplitude of Pressure Wave o The displacement wave in the medium is: s(x,t) = s max sin(kx - ω t) o The pressure wave in the medium is: P(x,t) = Δ P max cos(kx - ω t)

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The Speed of Sound o Like other mechanical waves, sound has a particular speed in a medium: v air = 331 m/sec + (0.6 m/sec/°C) T C v air = 343 m/sec at 20°C Speed increases as temperature increases o More dense media (solid, liquid) have faster sonic speeds v water 1493 m/sec v Fe 5130 m/sec
Observer in Motion o v is the speed of sound. If you (an observer) are moving at speed v o towards a sound the apparent speed of that sound will be v + v o . (if you are moving away from the sound then v o is negative). o The distance between crests (the wavelength λ ) is the same, but they arrive more often because of the boost in speed. Stationary observer: f’ = frequency observer hears: V o > 0 => towards sound, higher frequency. V o < 0 => away from sound, lower frequency.

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Source in Motion o If the source is moving relative to the medium, each crest is emitted from a position x = v s T to the right of the previous one. T= the period, is the same. o V s > 0 if source is approaching . o A stationary observer detects the waves with a different wavelength λ than they were emitted V s > 0 (approaching) => higher frequency V s < 0 (receeding) => lower frequency
The Doppler Effect o This shift in frequency is called the Doppler Effect Applies to all waves, including light o If both source and observer are moving: o Velocities are measured relative to the medium; v obs , v src positive if source and observer approaching each other; negative if moving away from each other obs source v v f f v v ! " + # = \$ % (

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Things to remember V o > 0 observer is moving towards source V s > 0 source is moving towards observer Moving towards source or observer always increases
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Lecture 6 - Mech. Waves (Ch. 13.7-13.8) - Lecture 6(Ch 13...

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