Question

Microwaves of frequency $3\times {10}^{4}MHz$ and ultrasonic waves of wavelength $1cm$ are passed through a slit of width $2cm$. Then

• A. diffraction will occur only in microwaves
• B. diffraction will occur only in ultrasonic wave
• C. diffraction will occur in both but diffraction pattern will be different
• D. diffraction will occur in both and diffraction patterns will be identical

Answer 1

The correct option is D diffraction will occur in both and diffraction patterns will be identical

We have: $C=\nu \lambda$
The wavelength of the microwaves is given by:
${\lambda }_m=\frac{3\times {10}^8}{3\times {10}^4\times {10}^6}={10}^{-2}m=1cm$
The wavelength of the microwave is $1cm$. Also the wavelength of ultrasonic wave is $1cm$. Both the waves have wavelengths less than the slit width. So, diffraction will occur for both the waves.
Since the two wave systems have the same wavelength, their diffraction patterns will be the same for the same slit.