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A. Whistling Robot A kid is sitting on the floor playing with a remote control robot that is whistling at a frequency of 14.3 kHz. (a) What is the period of the robot's whistle? Period = usec J (b) What is the speed of the sound wave if the air temperature is 21C? Wave Speed = y (c) What is the wavelength of the sound wave in the air? Wavelength = J A. SOLUTIONS (a) The period is the inverse of the frequency. T= i = 13 = 6.993 x1U_5 sec = 69.93 x10_8 sec = 69.93 psec f 14.3 x 10 Hz (b) The speed of sound in the 21 \"C air is c = 331.4 rnl's + (0.6 m!s}(21} = 344.0 rnls. (c) You know the sound speed and the frequency so use the dispersion equation to nd the wavelength. B. Doppler Shift - Case 1 What trequency whistle does the kid hear if the robot is moving directly away at a speed of2.58 mis? (a) The kid is a stationary observer : . J The robot is a _. y {b} Which equation should you use? fo=5_ (c) What is the frequency of the whistle heard by the f0 = {d} Calculate the doppler shi oi the whistle heard by the kid. 6. Doppler Shift - Case 2 The robot turns around and heads straight toward the kid at twice its previous speed. What frequency whistle does the kid hear now? (a) The kid is a stationary observer . y The robot is a _. y (b) Which equation should you use? fo=_c:5_ f0:_CfS_ ffh'i fo_i' c v cv c c (c) What frequency whistle will the kid hear now? to:- (d) Calculate the doppler shift of the whistle heard by the kid. Appointments 065-300 . WK-10 The solutions are all correct the only possible reason for any disparity in the solution 10 may be the value of c. If we take Jc = 342 m /s 11 B / c ) f = cf fs = 14 . 3 x 10 ' Hz 12 Ctv 2 3 42 x 14. 3 x 103 342+ 2.58 ~ 14 . 19 k H 2 d ) f 2 2vfs 2x 2 .58 X 14. 3x 105 342 07 10 C 066-299 SUNDAY 2 215.754 Hz 11 12 of of fo 2 ( V2 2 x 2, 58 2 5.16 m/s) C - V 349 X 14 . 3 x 10 = 14 . 52 KH2 7 342 - 5.16 d) 2 2ute 2 2 X 205. 16 X 14.3 x103 C 342 = 431.508 H2