Answer:
39.05°
Explanation:
As we know that, the diffraction is the phenomena of bending of light when it passes through an obstacle.
Mathematically,
[tex]dsin\theta=n\lambda[/tex]
Here, d is slit width, [tex]\lambda[/tex] is the wavelength, n is the order, [tex]\theta[/tex] is the angle.
Given that, d is 84 cm, n is 2, and the wavelength can be calculated as,
[tex]\lambda=\frac{c}{f}[/tex]
Here, c is the speed of sound and f is the frequency of sound wave.
Here, c is 343 m/s and f is 1300 Hz,
Therefore,
[tex]\lambda=\frac{343 m/s}{1300 Hz}\\\lambda=0.264m[/tex]
Recall diffraction equation in term of [tex]sin\theta[/tex].
[tex]sin\theta=\frac{n\lambda}{d}[/tex]
Put all the variables.
[tex]sin\theta=\frac{2\times 0.264 m}{84 cm}\\sin\theta=\frac{2\times 0.264 m}{0.84 m}\\\theta=39.05^{\circ}[/tex]
Therefore, it is the required angle between the first 2 order of diffraction.
