Question #165717

Suppose you are located 180 m from a radio transmitter.What if this station is 98.1 FM? (The FM band frequencies are in megahertz.)


1
Expert's answer
2021-02-22T10:19:24-0500

Radio waves are the electromagnetic waves, so the velocity of the radio waves is 3×108m/s3\times 10^{8}m/s .

The frequency of 98.1FM98.1FM  band (in megahertz) is 98.1×106Hz98.1 \times 10^6 Hz .

Now, Substitute  98.1×106Hz98.1\times10^6 Hz for ff  and 3.0×108m/s3.0 \times10^8 m/s  for vv in the equation λ=vf\lambda = \dfrac{v}{f}

λ=3.0×108m/s98.1×106Hz=3.058m\lambda= \dfrac{3.0\times10^8m/s}{98.1\times10^6Hz}=3.058m

Now, Substitute 3.058m for λ\lambda in the equation, nλ=180n\lambda=180 m

\because nλ=180n\lambda = 180

So, n=180λn= \dfrac{180}{\lambda}


=1803.058 =58.56= \dfrac{180}{3.058}\ =58.56

Round off to the three significant digits,

n=58.9n=58.9

Hence, the number of wavelengths present between radio station and you are 58.9 or 60(approx.)



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