**Question 12**

Two waves are represented by the following equations | |

a) | Calculate the velocities of the two waves. |

b) | If these two waves move along the same string, what will be the distance between two adjacent nodes of the standing wave which they produce? |

**Question 13**

A stationary wave is represented by the following equation | |

y = (1·5×10
^{-3})sin(1500t)cos(4·41x) | |

a) | What is the amplitude of oscillation at an anti-node? |

b) | What is the wavelength of the travelling waves which produced this stationary wave? |

c) | What type of wave is this? (light wave, sound wave, water wave etc) Explain your choice. |

**Question 14**

Young’s experiment is performed using a white light source with a red filter placed in front of it. The experiment is performed in a completely dark room so that very low levels of light can be observed. | ||

a) | Describe and explain the pattern which is observed on the screen. | |

b) | How will the pattern change if the red filter is removed and a blue filter is put in its place? | |

c) | What will be seen on the screen if one of the slits is covered with: | |

i) | a piece of metal | |

ii) | a thin sheet of transparent plastic of refractive index n = 1·5 | |

d) | What will be seen on the screen if the red and blue filters are put in front of the light source at the same time? | |

N.B. refractive index, n, of a medium is defined as follows | ||

where | ||

c = speed of light in vacuum and | ||

v = speed of light in the medium |

**Question 15**

A diffraction grating produces an image at an angle of 12·47° to the normal. The wavelength of the light being used is 600nm. The next order image is at an angle of 16·74° to the normal. Calculate: | |

a) | the order of the image at 12·47° |

b) | the number of lines per millimetre on the grating |

c) | the maximum order of image which could be observed (using this grating and light of wavelength 600nm). |

**Question 16**

A car is being driven towards a cliff at 100kmh^{-1}. The horn is sounded for a short time. The frequency of the horn is 440Hz. | |

An echo from the cliff is heard by the driver of the car and also by a stationary observer. If the speed of sound is 340ms^{-1}, calculate the apparent frequency of the echo as perceived by | |

a) | the stationary observer and |

b) | the driver of the car. |

**Question 17**

It can be shown that the relative Doppler shift for electro-magnetic radiations like light, radio waves etc is given (approximately) by |

where c is the speed of light and v is the relative speed of source and observer. |

The speed of a car is being measured by a police-person (note the gender neutral tone of this question) using a "radar speed-measuring thing". The frequency of the transmitted signal is 5GHz. When "mixed" the transmitted and received signals beat with a frequency of 750Hz. If the speed limit for the road is 110kmh^{-1}, should the driver be fined or not? |

**Question 18**

Plane waves on the surface of a liquid are generated by an oscillator of time period, T = 0·1s and amplitude 2mm. The speed of propagation of the waves is 20cms^{-1}. | ||

a) | Calculate the wavelength. | |

b) | At time t, point A (a point on the surface of the liquid near the oscillator) has displacement 2mm upwards. At time t, what will be the displacement of | |

i) | point B, which is 7cm away from point A (measured along the direction of propagation of the waves) | |

ii) | point C, which is 10·5cm away from point A (measured along the direction of propagation of the waves) | |

iii) | point D, which is 10cm away from point A (measured along the direction of propagation of the waves) | |

c) | Explain why your answers to parts b) i) and b) iii) above are approximate. |

**Question 19**

The speed, v, of propagation of a wave along a string/spring/wire under tension depends on the tension, T_{e} and the mass per unit length of the string/spring/wire, µ. |

Assuming that no other factors are involved, suggest a possible equation relating v, T_{e} and µ. Explain how you arrived at the equation. (You should be able to justify your suggestion by considering the units of the three quantities, v, T_{e} and µ.) |