Question

(a) Two microwave frequencies are authorized for use in microwave ovens, 875 and 2565 MHz. Calculate the wavelength (in cm) of each. cm (frequency = 875 MHz) cm (frequency = 2565 MHz)(b) Which frequency (in MHz) would produce smaller hot spots in foods due to interference effects? MHz

Answer 1

Given:

The two microwave frequencies are

$\begin{gathered} f_1=875\text{ MHz} \\ =875\times10^6\text{ Hz} \end{gathered}$

$\begin{gathered} f_2=\text{ 2565 MHz} \\ =2565\text{ }\times10^6\text{ Hz} \end{gathered}$

Required:

(a) Wavelength of each wave in cm.

(b) Choose the frequency that produces smaller hot spots in food.

Explanation:

(a) The wavelength of the wave can be calculated by the formula

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

Here, c is the speed of light whose value is

$c=3\times10^8\text{ m/s}$

The wavelength for the first frequency is

$\begin{gathered} \lambda_1=\frac{3\times10^8\text{ m/s}}{875\times10^6\text{ Hz}} \\ =34.29\text{ cm} \end{gathered}$

The wavelength for the second frequency is

$\begin{gathered} \lambda_2=\frac{3\times10^8\text{ m/s}}{2565\times10^6\text{ Hz}} \\ =\text{ 11.7 cm} \end{gathered}$

(b) The smaller wavelength will produce smaller hot spots.

As the frequency 2565 MHz has more smaller wavelength than 875 MHz, so the 2565 MHz will produce smaller hot spots.

Final Answer:

(a) Wavelength of 875 MHz is 34.29 cm and the wavelength of 2565 MHz is 11.7 cm

(b) The frequency 2565 MHz produces smaller hot spots in food as it has smaller wavelength.