Question

An electric charge oscillating with a frequency of 1 kilo cycles/s can radiates electromagnetic waves of wavelength (A) $100\mathrm{km}$ (B) $200\mathrm{km}$ (C) $300\mathrm{km}$ (D) $400\mathrm{km}$

Short answer

The wavelength of the radiated electromagnetic waves emitted by an electric charge oscillating with a frequency of 1 kilo cycles/s can be found using the formula $c=f\cdot \lambda$, where 'c' is the speed of light, 'f' is the frequency, and '$\lambda$' is the wavelength. By substituting the given values, we find the wavelength to be $300km$. Thus, the correct answer is (C) 300 km.

Step-by-step solution

Write down the given information and formula

We are given the frequency (f) of the oscillating electric charge as 1 kilo cycles/s or 1000 cycles/s. So, $f=1000Hz$ Also, we know that the speed of light (c) is approximately $3\cdot {10}^{8}m/s$. The formula that relates frequency, wavelength, and the speed of light is: $c=f\cdot \lambda$ where 'c' is the speed of light, 'f' is the frequency, and '$\lambda$' is the wavelength.

Solve for wavelength

We know the frequency (f) and the speed of light (c), so we can find the wavelength by rearranging the formula: $\lambda =\frac{c}{f}$ Now, plug in the values of 'c' and 'f': $\lambda =\frac{3\cdot {10}^{8}m/s}{1000Hz}$

Calculate the wavelength

Now, calculate the wavelength: $\lambda =\frac{3\cdot {10}^8}{1000}$ $\lambda =3\cdot {10}^{5}m$ Since 1 km = 1000 m, $\lambda =\frac{3\cdot {10}^{5}m}{1000}=300km$

Compare with the options and choose the correct one

Comparing the calculated value of the wavelength with the given options, we can see that the correct answer is: (C) 300 km

Key concepts

Frequency

Frequency is a fundamental concept in wave physics, describing how often a wave cycles or oscillates over a fixed duration of time. For electromagnetic waves, frequency is measured in hertz (Hz), which represents cycles per second. When an electric charge oscillates, it creates electromagnetic waves with a specific frequency. In the original exercise, the frequency is given as 1 kilo cycle per second, which equals 1000 Hz.

• Understanding frequency is crucial because it directly affects how we perceive electromagnetic waves, such as visible light, radio waves, and microwaves.
• The frequency range of electromagnetic waves is vast, ranging from very low frequencies like radio waves to very high frequencies such as gamma rays.
• Frequency plays an essential role in communication technologies, where different frequencies are used for different types of data transmission.

Knowing the frequency helps us characterize electromagnetic waves and understand how they interact with various materials.

Wavelength

Wavelength is the distance between consecutive peaks or troughs of a wave. It is a critical parameter in understanding wave behavior and is commonly denoted by the Greek letter $\lambda$. Wavelength is inversely related to frequency, meaning that as frequency increases, wavelength decreases.

• For electromagnetic waves, the wavelength can range from millimeters, like infrared light, to kilometers, such as radio waves.
• In terms of the original exercise, we used the formula $\lambda =\frac{c}{f}$ to calculate the wavelength of the electromagnetic wave given the frequency.
• Understanding wavelength allows us to distinguish between different types of electromagnetic radiation. For example, visible light has wavelengths between 400 and 700 nanometers.

Wavelength is especially important in applications like optics and telecommunications, where it helps determine how waves interact with surfaces and transmit through materials.

Speed of Light

The speed of light is a crucial constant in physics, representing how fast electromagnetic waves travel in a vacuum. It is approximately $3\cdot {10}^8\text{m/s}$. The speed of light is often denoted by 'c' and is fundamental to equations governing electromagnetic waves.

• The speed of light is essential for calculations involving electromagnetic waves, linking frequency and wavelength through the equation $c=f\cdot \lambda$.
• This constant speed means that light and other electromagnetic waves travel at the same velocity regardless of their frequency or wavelength when in a vacuum.
• In practical terms, understanding the speed of light is vital for fields like astronomy, where it helps measure vast cosmic distances, and in navigation systems such as GPS.

The speed of light sets a universal speed limit and plays a pivotal role in theories of relativity and our understanding of the universe.