A particular light source gives off light waves with a measured wavelength of
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The radio waves are electromagnetic wave, so it travels with velocity of light i.e .
We can use the relation between frequency, wavelength and speed as
Here c is speed of light, is wavelength and f is frequency and its value is given 99.90 FM, it is actually in megahertz (i.e 99.90 MHz).
Therefore,
.
Thus, the broadcast wavelength of the given radio station is 3.003 m.
data which is expressed in form of following way
here in above expression
= true value
= uncertainty in the value
now the relative uncertainty is given as
now by above formula we can say
a) 2.70 ± 0.05cm
here
True value = 2.70
uncertainty = 0.05
Relative uncertainty = = 0.0185
b) 12.02 ± 0.08cm
here
True value = 12.02
uncertainty = 0.08
Relative uncertainty = = 0.00665