Question

) Two microwave frequencies are authorized for use in microwave ovens: 900 and 2560 MHz. Calculate the wavelength of each.
(b) Which frequency would produce smaller hot spots in foods due to interference effects?
(c) Find the frequency range of visible light, given that it encompasses wavelengths from 380 to 760 nm.
(d) Approximately what is the smallest detail observable with a microscope that uses ultraviolet light of frequency ?

Answer 1

(a) Speed of microwave in free space = c = 3 x 10⁸ m / s.

For the frequency f = 900 MHz = 9 x 10⁸ Hz,

wavelength = = c / f = ( 3 x 10⁸ m / s ) / ( 9 x 10⁸ Hz ) = 0.33 m.

Similerly, for the frequency f = 2560 MHz = 2.56 x 10⁹ Hz,

wavelength = = c / f = ( 3 x 10⁸ m / s ) / ( 2.56 x 10⁹ Hz ) = 0.117 m.

(b) The microwave with 2560 MHz frequency will produce smaller hot spots in foods due to interference effects, because, a greater frequency or a smaller wavelength can produce an interference pattern of standing waves, whose antinodes, which are known as hot spots, are closer together, and hence, are closer in foods.