A person is able to hear sound waves within the frequency range of 20 Hz to 20 kHz . Determine the minimum and maximum wavelengths of sound audible to the person. Assume the speed of sound is 360 m s ⁻¹ .

Step-by-step solution

Given, speed of sound, v = 360 m s ⁻¹ Minimum frequency, f_ = 20 Hz Maximum frequency, f_ = 20 kHz = 20000 Hz The relation between speed, frequency, and wavelength is given by v = f = v f For minimum wavelength, frequency must be maximum: _ = v f_ = 360 20000 = 18 10⁻³ m = 18 mm For maximum wavelength, frequency must be minimum: _ = v f_ = 360 20 = 18 m Thus, the minimum and maximum wavelengths are 18 mm and 18 m respectively.