In Quincke's experiment, the sound intensity exhibits a minimum value I at a specific position. When the sliding tube is pulled out by a distance of 16.5 mm , the intensity rises to a maximum of 9 I . Taking the speed of sound in air as 330 m s ⁻¹ , determine the frequency of the sound source.

Step-by-step solution

In Quincke's tube experiment, when the sliding tube is pulled out by a distance x , the path difference between the two interfering sound waves changes by p = 2 x . The change in path difference required to transition from a minimum intensity to the adjacent maximum intensity is 2 . Equating the two expressions for the change in path difference: 2 x = 2 = 4 x Given x = 16.5 mm = 16.5 10⁻³ m , the wavelength is: = 4 16.5 10⁻³ m = 66 10⁻³ m The frequency of the sound source is given by: f = v Substituting v = 330 m s