In a location where the speed of sound is 337 m/s, a 2000 Hz sound wave impinges

Question

In a location where the speed of sound is 337 m/s, a 2000 Hz sound wave impinges on two slits 30cm apart. (a) At what angle is the first maximumlocated?
1°

(b) If the sound wave is replaced by 3.00cm microwaves, what slit separation gives the same angle for thefirst maximum?
2 cm

(c) If the slit separation is 1.00 µm, what frequency lightgives the same first maximum angle?
3 THz (a) At what angle is the first maximumlocated?
1°

(b) If the sound wave is replaced by 3.00cm microwaves, what slit separation gives the same angle for thefirst maximum?
2 cm

(c) If the slit separation is 1.00 µm, what frequency lightgives the same first maximum angle?
3 THz

Explanation / Answer

(a)     we use the form     d sin = m     the angle for the m = 1 maximum for the soundwaves is given by     = sin-1(m / d)        = sin-1[(m / d)(vsound / f)]        = .....o (b)     for = 3.0 cm microwaves the required slitspacing is given by     d = m / sin (c)     the wavelength is     = d sin / m     if this is light the frequency will be     f = c /       = .... Hz

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