## Tuesday, 23 September 2014

### WAVES QUESTIONS

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, Te 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, Te 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, Te and µ.)