# A-level Physics (Advancing Physics)/Signal Frequencies/Worked Solutions

**1. What is the frequency of an X-ray (wavelength 0.5 nm)?**

X-rays are electromagnetic waves, so they travel at the speed of light (3 x 10^{8} ms^{−1}).

3 x 10^{8} = f x 0.5 x 10^{−9}

**2. A sound wave, with a frequency of 44 kHz, has a wavelength of 7.7mm. What is the speed of sound?**

V = 44 x 10^{3} x 7.7 x 10^{−3} = 338.8ms^{−1}

**3. What is the fundamental frequency of the following signal?**

The big spike on the left is at approximately 750 Hz, so this is the fundamental frequency.

**4. Approximately how many harmonics does it contain?**

There are 14 other big spikes, plus a few other spikes which may be large enough to be harmonics.

**5. The three sine waves sin x°, 4sin(2x-50)° and 0.5sin(3x+120)° are added together to form a signal. What are the frequencies of each of the waves? What is the signal's fundamental frequency? Assume that the waves are travelling at the speed of light, and that 60° = 1mm**

sin x° has a wavelength of 360°. Using this, we can calculate the wavelengths of the other two waves, since f(ax) stretches f(x) by the reciprocal of a on the x axis. The frequency of each wave is given by the formula:

Wave (y=) | Wavelength (°) | Wavelength (mm) | Frequency (GHz) |
---|---|---|---|

sin x° | 360 | 6 | 50 |

4sin(2x-50)° | 180 | 3 | 100 |

0.5sin(3x+120)° | 120 | 2 | 150 |

sin x° has the lowest frequency, so 50 GHz is the fundamental frequency of the signal.