Question

The range of human hearing extends from approximately 20 Hz to 20000 Hz.

a. Find the wavelength for 43.2 Hz at a temperature of 34.7 ?C. Assume the velocity of sound at 0?C is 331 m/s. Answer in units of m

b. Find the wavelength for 1960 Hz at a temperature of 34.7 ?C. Answer in units of cm

Answer 1

lower frequency limit , f_lower = 20 Hz

higher frequency limit , f_higher = 20,000 Hz

a)

V_o =speed of sound at 0 C = 331 m/s

speed of sound at any temperature "T" is given as :;

V = V_o + (0.6)T

at T = 34.7 C ,

V = 331 + (0.6) (34.7)

V = 351.82 m/s

frequency , f = 43.2 Hz

so wavelength is given as ::

$\lambda$ = V/f

$\lambda$ = 351.82 / (43.2)

$\lambda$ = 8.144 m

b.

at T = 34.7 C , speed of sound , V = 351.82 m/s

frequency , f = 1960 Hz

so wavelength is given as ::

$\lambda$ = V/f

$\lambda$ = 351.82 / (1960)

$\lambda$ = 0.1795 m

$\lambda$ = 17.95 cm

$\lambda$ = 8.144 m