Question

Diffraction of sound waves is demonstrated when sound waves with a frequency of 1300 Hz from a distant source are diffracted through a doorway which is 84 cm wide. Calculate the angle between the first two orders of diffraction taking the speed of sound to be 343 m/s.

Answer 1

Answer:

39.05°

Explanation:

As we know that, the diffraction is the phenomena of bending of light when it passes through  an obstacle.

Mathematically,

$dsin\theta=n\lambda$

Here, d is slit width, $\lambda$ is the wavelength, n is the order, $\theta$ is the angle.

Given that, d is 84 cm, n is 2, and the wavelength can be calculated as,

$\lambda=\frac{c}{f}$

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,

$\lambda=\frac{343 m/s}{1300 Hz}\\\lambda=0.264m$

Recall diffraction equation in term of $sin\theta$.

$sin\theta=\frac{n\lambda}{d}$

Put all the variables.

$sin\theta=\frac{2\times 0.264 m}{84 cm}\\sin\theta=\frac{2\times 0.264 m}{0.84 m}\\\theta=39.05^{\circ}$

Therefore, it is the required angle between the first 2 order of diffraction.