Question

A ratio can tune in to any station in the $7.5MHz$ to $12MHz$ band. What is the corresponding wavelength band?

Answer 1

The relation between frequency and wavelength comes in many different forms, and is all-important in understanding how waves behave.
The relation tells us many things about how fast waves move too, allowing us to compute quantities like phase velocity and group velocity
The relation between frequency and wavelength in waves is so important that it has a special name, known as the dispersion relation.

Complete step by step solution:
The wavelength is the distance between one wave peak and the next wave peak is known as the wavelength or the distance between one wave high point and the next high point.
Let us consider the ocean waves where we can observe the top of one wave and the top of the next wave. The wavelength is the distance between these two wave tops or peaks. With waves in the ocean, the frequency of the waves will be the number of times that a wave peak crosses any given point on the ocean.
We know that the velocity of the wave is the multiplication of frequency and wavelength.
We have to calculate the wavelength for $7.5MHz$
Wavelength= velocity of wave/ frequency
$\lambda = \dfrac{{300}}{{12}} = 25m$
After simplification, the above equation will be,
$\lambda = \dfrac{{300}}{{7.5}} = 40m$
Now calculating the frequency for $12MHz$
$\lambda = \dfrac{{3 \times {{10}^8}}}{{12 \times {{10}^6}}}$
Now simplify the above equation,
$\lambda = \dfrac{{300}}{{12}} = 25m$
Hence the wavelength ranges from $25m$ to $40m$.

Note:
The wavelength and frequency are inversely proportional to each other
The greatest frequency of waves having a short wavelength.
The one-half the wavelength means twice the frequency. so, the wavelength ratio and frequency ratio are inverse to each other.