Question

Consider a medium where the speed of sound is 354 m/s. In this medium, a 2000 Hz sound wave is incident on two slits 30.0 cm apart. This creates an interference pattern on a distant screen. In analogy to double slit interference of light waves, the equation d sin ✓ = m can be used to find the location of the maxima, in the same way that it does for Young's double slit experiment with light.

(a) At what angle is the first maximum located? State your answer in degrees.

(b) If the slit separation is 1.00 µm instead and light waves are used instead of sound waves, what frequency of light gives the same first maximum angle as in (a)?

(c) How many maxima are there on the screen in case (a) (counting the maximum at the centre and the maxima on both sides of the center)? How many maxima are there in case (b)?

Answer 1

(a)

first, we find the wavelength

= v / f = 354 / 2000 = 0.177 m

so,

dsin = m

0.3 * sin = 1 * 0.177

= arcsin ( 0.177 / 0.3)

= 36.2 degrees

_______________________

(b)

dsin = m

= dsin / m

= 1e-6 * sin 36.2 / 1

= 591e-9 m

so,

f = c /

f = 3e8 / 591e-9

f = 5.08e14 Hz

______________________________

(c)

the maximum value that sin   can have is 1, for an angle of 90 degree

so,

m = dsin /

m = 0.3 * 1 / 0.177

m = 1.69

so,

largest value of number of maxima = 1