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Q.

The faintest sound, the human ear can detect at a frequency of 1 kHz (for which ear is most sensitive) corresponds to an intensity of about 10-12w/m2. Assuming the density of air = 1.5 kg/m3 and velocity of sound in air ≅ 300 m/s, the pressure amplitude and displacement amplitude of the sound will be respectively _N/m2 and m.

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a

3×10-5Pa, 13π×10-10m

b

2×10-5 Pa, 23π×10-10m

c

5×10-5 Pa, 1π×10-10m

d

5×10-5 Pa, 43π×10-10m

answer is A.

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Detailed Solution

I = Pm22ρV10-12 = Pm22(1.5)(300)Pm = 3×10-5 PaPm = BAK = (ρV2)A2π(vf)Pm = (2πρVf)A3×10-5 = (2π)(1.5)(300)(103)AA = 13π×10-10 m

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The faintest sound, the human ear can detect at a frequency of 1 kHz (for which ear is most sensitive) corresponds to an intensity of about 10-12w/m2. Assuming the density of air = 1.5 kg/m3 and velocity of sound in air ≅ 300 m/s, the pressure amplitude and displacement amplitude of the sound will be respectively ___N/m2 and __ m.