Question

Radio waves that vibrate 160,000,000 times per second are used on some train lines for communications. If radio waves that vibrate half as many times per second were used instead, how would the wavelength change?

Answer 1

New wavelength `lambda=3,75m`, is double its original value after the frequency was halved, according to one of the general wave equations `c=flambda`.

Explanation:

Frequency is the number of complete cycles per second.
So `160000000` vibrations per second is equivalent to a frequency of `f=160MHz`.
So half this frequency would be `80MHz`.

Since radio waves are electromagnetic in nature, they travel at the speed of light `c=3xx10^8m//s`.

We may use one of the general wave equations to find the corresponding wavelength :

`c=flambda` and hence `lambda=c/f`.

`therefore lambda=(3xx10^8m//s)/(80xx10^6Hz)=3,75m`.

The wavelength would hence be double the value as what it initially was. (Wavelength is the minimum distance between any 2 points which are in phase).