Question

Question 4 (a) A sound wave with a frequency of 250 Hz is transmitted through air at 25° C (298.2K). The specific gas constant for air is 287 J/kg K, and the specific heat ratio is y = 1.40. Determine: (i) (ii) The speed of sound, The wavelength, The wave number, The angular frequency for this condition. (iii) (iv) [8 Marks] (b) The noise level measured at a particular location in a factory with a noisy machine operating nearby is 92 dB(A). When the machine is turned off, the noise level measured at the same location is 88 dB(A). Determine: (i) In the unit dB(A), what does (A) mean? (ii) What is the noise level due to the machine alone? (C) A police car's siren gives out a note of wavelength 0.20 m when it is stationary. The car drives towards you at 13 m/s. Determine: (i) Will the sound frequency shift to a higher or lower value when the car drives towards you?

Please answer all parts of Part (b)

please only answer if you can do so correctly, and showing working out.

Answer 1

a.

i.

v = sqrt (k R T)

v = sqrt (1.4 * 287 * 298.2)

v = 346.1455 m/s

ii.

Wavelength = v / f

Wavelength = 346.1455 / 250

Wavelength = 1.384582‬ m

iii.

Wavenumber = 2 pi / wavelength

Wavenumber = 2 * pi / 1.384582‬

Wavenumber = 4.5379

iv.

w = 2 pi f

w = 2 * pi * 250

w = 1570.7963 rad/s

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