5. -1 points SerPSE9 37. P.010 My Notes Ask Your Teacher Light with a wavelength

Question

5. -1 points SerPSE9 37. P.010 My Notes Ask Your Teacher Light with a wavelength 438 nm passes through a double-slit system that has a slit separation d 0.700 mm. Determine how far away a screen must be placed in order that a dark fringe appear directly opposite both slits, with just one bright fringe between them. Cm Need Help? Read it 6. -13 points SerPSE9 37. P.012. My Notes Ask Your Teacher In a location where the speed of sound is 336 m/s, a 2000-Hz sound wave impinges on two slits 26.0 cm apart. (a) At what angle is the first maximum of sound intensity located? (b) If the sound wave is replaced by 2.75-cm microwaves, what slit separation gives the same angle for the first maximum of microwave intensity? Cm (c) If the slit separation is 1.00 Hm, what frequency of light gives the same angle to the first maximum of light intensity? THz Need Help? Read it

Explanation / Answer

a)

v = f * lambda

lambda = v / f = 336 / 2000

lambda = 0.168 m

the for the angle at maximum

D*sin(theta) = m * lambda

theta = sin^-1( m * lambda / D)

theta = sin^-1( 1 * 0.168 / 0.26)

theta = 40.25 deg

b)

the maximum angle for new separation distance

d*sin 40.25deg = 1 * 0.0275

d = 0.0275 / sin(40.25deg)

d = 0.04256 m

c)

here also

d * sin(theta) = m * ( v/f)

f = m * v / ( d * sin(theta) )

f = 1 * 336 / ( 0.04256 * sin(40.25 deg)

f = 12219 Hz

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