Question

Two microwave frequencies are authorized for use in microwave ovens: 900 and 2560 MHz. Calculate the wavelength of each.

a) 2.998 x 108 m/s / 900 MHz
b) 2.998 x 108 m/s / 2560 MHz
c) 900 MHz/2.998 × 108 m/s
d) 2560 MHz/2.998 × 108 m/s

Answer 1

To calculate the wavelength of microwave frequencies, we use the speed of light divided by the frequency. For 900 MHz the wavelength is 33.3 cm, and for 2560 MHz it is 11.7 cm. The higher frequency of 2560 MHz would result in smaller hot spots in food.

Step-by-step explanation:

Calculation of Wavelengths in Microwaves

To calculate the wavelength of microwave frequencies, we use the formula for wave speed in a vacuum where speed (c) equals wavelength (λ) times frequency (f). The formula is c = λ * f, which can be rearranged to λ = c / f when solving for wavelength. Here, c is the speed of light, approximately 2.998 x 108 m/s.

1. For 900 MHz microwaves, the calculation is λ = 2.998 x 108 m/s / 900 x 106 Hz, yielding a wavelength of roughly 33.3 cm.
2. For 2560 MHz microwaves, the calculation is λ = 2.998 x 108 m/s / 2560 x 106 Hz, yielding a wavelength of roughly 11.7 cm.

As for part (b) of the question, the microwave oven that operates at 2560 MHz would produce smaller hot spots in foods due to interference effects because it has a smaller wavelength. This wavelength corresponds to the higher frequency, 2560 MHz.