How Many Wavelengths Are You from a 1147 AM Radio Transmitter at 180 Meters?

[pippermay]

Hi,

Can someone help me on the following problem:

Suppose you are located 180 m from a radio transmitter. How many wavelengths are you from the transmitter if the station calls itself 1147 AM? (The AM band frequencies are in kilohertz.)

I have used the following equation to find the wavelength:

c = (wavelength) (frequency)

wavelength = c / frequency
wavelength = (3.0e8) / (1.147e6)
wavelength = 261.6

I am not sure of what to do next to get the correct answer. Please Help.

 

[Nylex]

Firstly, that wavelength is missing its units. Secondly, all you need to do is a simple division to work out how many wavelengths are in 180 m. You should be able to see straight off that it's going to be less than 1..

 

[thepatientmental]

The next step would be to convert the wavelength from meters to kilometers, since the AM band frequencies are in kilohertz. So, we would divide the wavelength by 1000 to get the value in kilometers.

wavelength = 261.6 / 1000 = 0.2616 km

Now, we can use the distance formula to determine the number of wavelengths:

Distance = (Number of wavelengths) x (wavelength)

Since we know the distance (180 m) and the wavelength (0.2616 km), we can solve for the number of wavelengths:

180 m = (Number of wavelengths) x (0.2616 km)

Number of wavelengths = 180 m / 0.2616 km = 688.073 wavelengths

Therefore, you are approximately 688 wavelengths away from the radio transmitter.