Question

The highest frequency that a healthy ear can typically hear is 2.0 × 104 Hz. Assume that a sound wave with this frequency travels at 344 m/s and passes through a doorway that has a width of 1.0 m. (a) Determine the angle that locates the first minimum to either side of the central maximum in the diffraction pattern for the sound. (b) Suppose that yellow light (wavelength = 570 nm, in vacuum) passes through a doorway and that the first dark fringe in its diffraction pattern is located at the angle determined in part (a). How wide would this hypothetical doorway have to be?

Answer 1

a) given
f = 2.0*10^4 hz
v = 344 m/s

let lamda is the wavelength of the sound wave.

we know, v = lamda*f

==> lamda = v/f

= 344/(2.0*10^4)

= 0.0172 m

d = 1.0 m

for first order minimum, d*sin(theta) = lamda

sin(theta) = lamda/d

sin(theta) = 0.0172/1

theta = sin^-1(0.0172)

= 0.986 degrees <<<<<<<<<<---------------Answer

b) lamda = 570 nm = 570*10^-9 m

d = ?

d*sin(theta) = lamda

d = lamda/sin(theta)

= 570*10^-9/sin(0.986)

= 3.31*10^-5 m <<<<<<<<<<---------------Answer