During Quincke's experiment, the detected sound transitions from a maximum to a minimum as the sliding tube is shifted by a distance of 2.50 cm . Determine the frequency of the sound, given that the speed of sound in air is 340 m s ⁻¹ .

Step-by-step solution

In Quincke's tube experiment, when the sliding tube is moved by a distance x , the path difference between the two interfering sound waves changes by 2x . For the sound intensity to transition from a maximum to a minimum, the change in path difference must be 2 . Equating the two expressions for the change in path difference: 2x = 2 = 4x Given x = 2.50 cm = 0.025 m , the wavelength is: = 4 0.025 = 0.1 m The frequency of the sound wave is given by f = v . Substituting v = 340 m s ⁻¹ and = 0.1 m : f = 340 0.1 = 3400