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Unformatted text preview: s focus on harmonic waves.
(a) For fixed average intensity, how do the amplitude of (i) the molecular displacements
sm and (ii) pressure pm vary with the frequency of a sound wave?
(b) Two 1 kHz sound waves, one propagating in water (B=2.2 x 109 Pa, v=1480 m/s)
and one in air (B=1.4 x 105 Pa, v=343 m/s) have equal average intensities. What is
the ratio of the (i) the molecular displacements sm and (ii) the pressure modulations
pm for these two waves? Does your answer make sense? (Explain briefly).
(c) The perceived loudness of a sound wave is roughly proportional to the sound level,
given by β(in dB)=10 log10 (I/I0), where I0=10-12 W/m2 corresponds to the threshold of
hearing. (Note that β is dimensionless, but we express it in fake "units" of decibels
(dB); this just means that we've calculated 10 log10 (I/I0). ) Suppose that you have a
1 W point source of sound waves, and that there are no floors, walls or other objects
nearby to reflect the sound.
(i) If you double your distance r from the source, what happens to the sound level,
and thus to the loudness...
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