Question

Radio station klbj broadcasts at a frequency of 93.7 mhz. determine the length of the waves that corresponds to this frequency.

Answer 1

The Answer in significant figures is 3.20 meters. The full Answer is 3.201707577*10^0 meters

Step-by-step explanation:

You must first convert 93.7Mhz to hz: 93.7mhz * 10^6hz/1Mhz = 9.37*10^7.

Next, since all EM waves' frequency and wavelength = the speed of light(c)(3.00*10^8m/s), insert the new frequency (hertz) into the formula below and solve for Wavelength (lambda)

c=(lambda)(hertz), manipulate the equation to solve for wavelength (lambda)

(lambda)=(C) / (hertz) ; Hertz = hz = s^-1 or 1/s

lambda = 3.00*10^8m/s / 9.37*10^7hz (^^remember hz = 1/s)

Since hz = 1/s, both of the factors have 1/s in the variables' place, so the 1/s cancels and your left with m (meters)

= 3.201707577 meters

Answer 2

The wavelength (in m) of a periodic wave is equal to the velocity of the wave (in m/s) divided by the frequency (in Hz). When talking about radio waves (electromagnetic radiation) that velocity is the speed of light, or 299792458 meters per second. Given a frequency of 93.7 MHz, or 93700000 Hz, the wave length is 299792458/93700000, or 3.1994926m.