Question

In addition to cable and satellite broadcasts, television stations still use VHF and UHF bands for digitally broadcasting their signals. Twelve VHF television channels (channels 2 through 13) lie in the range of frequencies between 54.0 MHz and 216 MHz. Each channel is assigned a width of 6.00 MHz, with the two ranges 72.0 – 76.0 MHz and 88.0 – 174 MHz reserved for non-TV purposes. (Channel 2, for example, lies between 54.0 and 60.0 MHz.) (a) Calculate the broadcast wavelength range for channel 5. (Enter your answers from smallest to largest.) X Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m (b) Calculate the broadcast wavelength range for channel 6. (Enter your answers from smallest to largest.) x Your response differs from the correct answer by more than 10%. Double check your calculations. m X Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m (c) Calculate the broadcast wavelength range for channel 8. (Enter your answers from smallest to largest.) X Your response differs from the correct answer by more than 10%. Double check your calculations. m X Your response differs from the correct answer by more than 10%. Double check your calculations. m

Answer 1

Speed of electromagnetic waves, c = f λ where f is the frequency and λ is the wavelength of the waves.

Wavelength of electromagnetic waves, λ = c/f

Speed of light in free space, c = 3 x 10⁸ m/s

For channel 5: f1 = 76 MHz ; f2 = 82MHz

Wavelength corresponds to f1 is λ1 = c/f1 = 3 x 10⁸/ 76 x 10⁶ = 3.947 m

Wavelength corresponds to f2 is λ2 = c/f2 = 3 x 10⁸/ 82 x 10⁶ = 3.658 m

The wavelength range are:

3.658 m

3.947 m

For channel 6: f1 = 82 MHz ; f2 = 88 MHz

Wavelength corresponds to f1 is λ1 = c/f1 = 3 x 10⁸/ 82x 10⁶ = 3.658 m

Wavelength corresponds to f2 is λ2 = c/f2 = 3 x 10⁸/ 88 x 10⁶ = 3.409 m

The wavelength range are:

3.409 m

3.658 m

For channel 8: f1 = 180 MHz ; f2 = 186 MHz

Wavelength corresponds to f1 is λ1 = c/f1 = 3 x 10⁸/ 180 x 10⁶ = 1.666 m

Wavelength corresponds to f2 is λ2 = c/f2 = 3 x 10⁸/ 186 x 10⁶ = 1.612 m

The wavelength range are:

1.612 m

1.666 m