Chapter 27, Problem 57A

When listening to a radio station broadcasting at 101 MHz (101 million wave vibrations per second), you wonder how long the wavelength of these waves is. What is the answer, and how does it compare to your height?

To determine

To determine the length of the wavelength of radio station broadcasting of 101 MHz and compare it with the human height.

Answer to Problem 57A

The length of the 101 MHz radio wave is 2.97 m and the amplitude of the wave is used to compare the human height.

Explanation of Solution

Given data:

Radio station broad casting(f )= 101×10⁶ cycles/second.

Formula used:

  $\lambda =\frac{c}{f}$ m.

Calculation:

We know that the wavelength of the wave is given by the equation,

  $\lambda =\frac{c}{f}$ m.

And, we know that the electro magnetic radiation travels at 3×10⁸m/s.

Substitute the values in the given equation (λ ).

  $=\frac{3\times {10}^8}{101\times {10}^6}$ m.

= 2.97 m.

The amplitude of a wave is called the height of the wave. Which is measured from the highest point on the wave called peak or crest and the lowest point of the wave called the trough. So, the amplitude of the wave is used to measure the height of human beings.

Conclusion:

The length of the 101 MHz radio wave is 2.97 m. The amplitude (height) of the wave gives us to compare our height.