Summary: In problem 3, we need to calculate the period of the microwave. The period is defined as the time taken for one complete cycle of oscillation. It is an important parameter that helps in understanding the behavior of the waves. The calculation of the period of a microwave involves knowledge of its frequency and wavelength.

### 1. Understanding Microwave Waves

Microwave waves are a type of electromagnetic wave with a frequency range of 1 GHz to 300 GHz. They are used for communication, cooking, and various industrial applications. Microwave ovens use microwave radiation to heat food by causing water molecules in the food to vibrate, generating heat. Microwave waves are similar to other electromagnetic waves like visible light and radio waves, but they have a shorter wavelength and higher frequency.

The frequency of a wave is the number of complete cycles that occur in one second. It is measured in hertz (Hz). The wavelength of a wave is the distance between two consecutive points on the wave that are in phase- in other words, the length of one complete cycle. The wavelength is measured in meters (m).

The relationship between the frequency and wavelength of a wave is given by the formula: wavelength x frequency = speed of light. The speed of light in a vacuum is approximately 3 x 10^8 m/s. Therefore, as the frequency of a wave increases, its wavelength decreases, and vice versa.

### 2. Calculation of Microwave Period

The period of a wave is calculated as the time taken for one complete cycle of oscillation. The formula for calculating the period of a wave is given by: Period = 1 / Frequency.

To calculate the period of a microwave, we first need to determine its frequency and wavelength. The frequency can be obtained from the specifications of the microwave or by using an instrument such as a frequency meter. The wavelength can be calculated using the formula: Wavelength = Speed of Light / Frequency.

Once we have obtained the frequency and wavelength, we can use the formula for period to calculate the time taken for one complete cycle of oscillation. For example, if the frequency of the microwave is 2.45 GHz (2.45 x 10^9 Hz) and the wavelength is 0.12 meters, then the period can be calculated as follows:

Period = 1 / Frequency

Period = 1 / 2.45 x 10^9

Period ≈ 4.08 x 10^-10 seconds

### 3. Importance of Period in Microwave Technology

The period of a microwave is an important parameter that helps in understanding the behavior of the waves. In microwave technology, the period is used in the design and operation of various devices such as antennas, filters, and amplifiers.

For example, the design of a microwave antenna depends on its operating frequency and the wavelength of the microwave. The size and shape of the antenna are determined by the wavelength, while the efficiency and power handling capacity depend on the frequency and period of the microwave.

Similarly, the design of a microwave filter depends on its cutoff frequency, which is the frequency below which the filter provides effective attenuation of unwanted signals. The cutoff frequency is related to the wavelength and period of the microwave, and therefore knowledge of the period is essential for the design of the filter.

### 4. Factors Affecting the Period of a Microwave

The period of a microwave is affected by several factors, including the frequency and wavelength of the wave, the properties of the medium through which it propagates, and the presence of any obstacles or interference.

As mentioned earlier, the frequency and wavelength of a wave are inversely proportional, so as one increases, the other decreases. Therefore, the period of a wave is also inversely proportional to its frequency and directly proportional to its wavelength.

The properties of the medium through which the microwave propagates also affect its period. For example, the speed of light is slower in a medium such as water than in a vacuum, which affects the wavelength and period of the microwave.

The presence of any obstacles or interference can also affect the period of a microwave. For example, if a microwave encounters a metal object, it can reflect or absorb the waves, which can create interference and change the period of the waves.

### Conclusion:

The period of a microwave is an important parameter that plays a crucial role in understanding the behavior of the waves and designing various devices used in microwave technology. It is calculated by using the formula for period and requires knowledge of the frequency and wavelength of the wave. The period of a microwave is affected by several factors, including the frequency and wavelength of the wave, the properties of the medium through which it propagates, and the presence of any obstacles or interference. Therefore, a proper understanding of the concept of period is essential for working with microwave technology.