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# A radio wave has a frequency of 8.01 × 108 s−1. What is its wavelength, in meters?

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A radio wave has a frequency of 8.01 × 108 s−1. What is its wavelength, in meters?

Guest Aug 1, 2014

#1
+4471
+8

speed = wavelength*frequency

wavelength = speed / frequency

wavelength = 3.0*10^8 m/s / 8.01*10^8 s^-1= 0.3745318352059925 = 3.75*10^-1.

AzizHusain  Aug 1, 2014
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#1
+4471
+8

speed = wavelength*frequency

wavelength = speed / frequency

wavelength = 3.0*10^8 m/s / 8.01*10^8 s^-1= 0.3745318352059925 = 3.75*10^-1.

AzizHusain  Aug 1, 2014
#2
+91927
+5

I always use the units to help me with 'rates' questions.

The speed of light in a vacuum is 299 792 458 m / s    I think radio waves travel at the same speed.

The frequency of the wave is 8.01*10^8  wavelengths/s.  This is the same as 1s/8.01*10^8  wavelengths

You want to know metres/wavelength

$$\frac{299792458m}{\not{s}}\times \frac{1\not{s}}{8.01*10^8\;wavelength}=\frac{299792458m}{8.01*10^8\;wavelength}$$

The seconds cancel out !

$${\frac{{\mathtt{299\,792\,458}}}{\left({\mathtt{8.01}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{8}}}\right)}} = {\mathtt{0.374\: \!272\: \!731\: \!585\: \!518\: \!1}}$$

$$Wavelength \;\approx 0.37 m$$

Melody  Aug 2, 2014

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