Determine the bulk modulus of air using the given data for a sound wave of wavelength 35 cm travelling in air. The pressure at a specific point fluctuates between (1.0 10^5 14) Pa , and the particles of the air undergo simple harmonic motion with an amplitude of 5.5 10⁻⁶ m .

Step-by-step solution

The pressure amplitude P_m of a sound wave is related to the bulk modulus B , the wave number k , and the displacement amplitude A by the relation: P_m = B k A The wave number k is given by k = 2 . Substituting this into the equation gives: P_m = B ( 2 ) A Rearranging for the bulk modulus B : B = P_m 2 A Given the values: Pressure amplitude, P_m = 14 Pa Wavelength, = 35 cm = 0.35 m Displacement amplitude, A = 5.5 10⁻⁶ m Substituting these values into the formula: B = 14 0.35 2 5.5 10⁻⁶ Using 22 7 : B = 4.9 11 22 7