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

Speed of sound v = 337m/s frequency of sound f =2000Hz So that the wave length is
          = v /f = 337 / 2000 = 0.1685m
distance between the slits d =3.0cm The path difference = d Sinm
where m is the angle for the mth fringe. a) The condition for maximumis                                         path difference = m                                                 0r d Sin m =m      for the firstorder m = 1 ,
   Therefore 1=Sin-1( / d )
   = sin-1 ( 0.1685 / 0.3)
   =34.17o
b) Here = ' =3cm      therefore thewidth of the slit d ' = ' / Sin1                                                      = 0.03 / sin34.17
                                                     = 0.0534 m
                                                     = 5.34 cm
c) All factors remaining the samed = d ' = 1*10-6m       Thewavelength of light   ' = d ' Sin1
                                              = 0.0534 * sin34.17
                                              = 0.0299 m
     Hence thefrequency of light f = c / '
                                                  = 3 x 108 / 0.0299
                                                  = 1 x 1010 Hz

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.