An AM station broadcasts rock music at "950 on your radio dial" Units for AM frequencies are given in kilhertz(kHz). Find the wavelength of the station's radio waves in meters, nanometers, and angstroms.
I don't understand that process, since the answer for the meters is supposed to be 316m
you would use 1 Hz =299792458wavelength meters
so using that you would convert kHz to Hz, then Hz to meters. for the radio wave in meters
then you would continue using the same conversion as the one above and then convert meters to nanometers using 1m= 1X10^-9 nm.
for the last one in angstroms. you use the conversion you left off of with meters and convert 1m=1X10^10 A.
Hope that helps:)
First of all do a quick approximation from general knowledge as 1 MHz has a wavelength of 300 m. Thus we expect that 950 kHz (0.950 MHz) will have a wavelength just longer than this.
f=950 kHz
use v=fl, velocity = frequency x wavelength
so l=v/f
velocity (speed of light) = 3 x 10^8 m s^-1
950 kHz = 950 x 10^3 s^-1
thus l=3 x 10^8 m s^-1/950 x 10^3 s^-1
so l=316 m
which is consistent with our approximation at the start.
To find the wavelength of the AM station's radio waves, we need to use the formula:
wavelength = speed of light / frequency
First, we need to convert the frequency from kilohertz (kHz) to hertz (Hz). We can do this by multiplying the frequency by 1000 since 1 kHz equals 1000 Hz.
Given that the frequency of the AM station is 950 kHz, when converted to Hz, it will be 950,000 Hz.
The speed of light is a constant value, approximately 3 x 10^8 meters per second (m/s).
Now we can calculate the wavelength:
wavelength = (3 x 10^8 m/s) / (950,000 Hz)
To simplify the calculation, we can express the speed of light in scientific notation:
wavelength = (3 x 10^8 m/s) / (9.5 x 10^5 Hz)
Combining the exponents:
wavelength = (3 / 9.5) x 10^(8 - 5) m
Now we can perform the division:
wavelength = 0.316 x 10^3 m
Finally, converting from scientific notation to decimal notation:
wavelength = 0.316 x 1000 m
wavelength = 316 meters (m)
To convert this wavelength to nanometers (nm), we need to multiply it by 10^9 since 1 meter equals 10^9 nanometers.
wavelength in nanometers = 316 m x 10^9 nm/m
wavelength in nanometers = 316,000,000,000 nm
And finally, to convert the wavelength to angstroms (Å), we need to multiply it by 10^10 since 1 nanometer equals 10 angstroms.
wavelength in angstroms = 316,000,000,000 nm x 10 Å/nm
wavelength in angstroms = 3,160,000,000,000 Å
So, the wavelength of the AM station's radio waves is approximately 316 meters, 316,000,000,000 nanometers, and 3,160,000,000,000 angstroms.