Calculate the wavelength in centimeters of (a) an airport tower transmitting at 118.6 MHz. (b) a VOR (radio navigation aid)transmitting at 114.10 kHz. (c)an NMR signal at 105 MHz. (d)an infrared absorption peak with a wavenumber of 1210cm^-1

To calculate the wavelength of electromagnetic waves, we can use the formula:<br /><br />\[ \lambda = \frac{c}{f} \]<br /><br />where \( \lambda \) is the wavelength, \( c \) is the speed of light in a vacuum (approximately \( 3 \times 10^8 \) m/s), and \( f \) is the frequency of the wave.<br /><br />Let's calculate the wavelength for each case:<br /><br />(a) For an airport tower transmitting at 118.6 MHz:<br /><br />\[ f = 118.6 \times 10^6 \text{ Hz} \]<br /><br />\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{118.6 \times 10^6 \text{ Hz}} \]<br /><br />\[ \lambda \approx 2.54 \text{ m} \]<br /><br />To convert this to centimeters:<br /><br />\[ \lambda \approx 2.54 \times 100 \text{ cm} \]<br /><br />\[ \lambda \approx 254 \text{ cm} \]<br /><br />(b) For a VOR transmitting at 114.10 kHz:<br /><br />\[ f = 114.10 \times 10^text{ Hz} \]<br /><br />\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{114.10 \times 10^3 \text{ Hz}} \]<br /><br />\[ \lambda \approx 2.63 \text{ m} \]<br /><br />To convert this to centimeters:<br /><br />\[ \lambda \approx 2.63 \times 100 \text{ cm} \]<br /><br />\[ \lambda \approx 263 \text{ cm} \]<br /><br />(c) For an NMR signal at 105 MHz:<br /><br />\[ f = 105 \times 10^6 \text{ Hz} \]<br /><br />\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{105 \times 10^6 \text{ Hz}} \]<br /><br />\[ \lambda \approx 2.86 \text{ m} \]<br /><br />To convert this to centimeters:<br /><br />\[ \lambda \approx 2.86 \times 100 \text{ cm} \]<br /><br />\[ \lambda \approx 286 \text{ cm} \]<br /><br />(d) For an infrared absorption peak with a wavenumber of 1210 cm\(^{-1}\):<br /><br />The wavenumber is the reciprocal of the wavelength in centimeters. Therefore, we can find the wavelength by taking the reciprocal of the wavenumber:<br /><br />\[ \lambda = \frac{1}{1210 \text{ cm}^{-1}} \]<br /><br />\[ \lambda \approx 0.000822 \text{ cm} \]<br /><br />So, the wavelength of the infrared absorption peak is approximately 0.000822 cm.