Sound emerges through a doorway, as in Figure 17.10. The width of the doorway is

Question

Sound emerges through a doorway, as in Figure 17.10. The width of the doorway is 85 cm, and the speed of sound is 343 m/s. Find the diffraction angle ? when the frequency of the sound is (a) 5.0 kHz and (b) 5.0

Sound emerges through a doorway, as in Figure 17.10. The width of the doorway is 85 cm, and the speed of sound is 343 m/s. Find the diffraction angle ? when the frequency of the sound is (a) 5.0 kHz and (b) 5.0 ? 10^2 Hz. Figure 17.10 Each vibrating molecule of the air in the doorway generates a sound wave that expands outward and bends, or diffracts, around the edges of the doorway. Because of interference effects among the sound waves produced by all the molecules, the sound intensity is mostly confined to the region defined by the angle theta on either side of the doorway. Figure 17.11 Because the dispersion of high frequencies is less than the dispersion of low frequencies, you should be directly in front of the speaker to hear both the high and low frequencies equally well.

Explanation / Answer

Using .. sin? = n?/a .. for the edge ot the central maxima of the diffracted sound .. n=1 locates the first minima marking the edge of the central maxima.

For 5.0^3 Hz .. ? = 343m/s / 5.0^3 Hz
a= 0.85m
sin ? = 1*(343/5.0^3) / 0.85 = 0.0891 .. .. .. ?? = 5.0

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