# Question Q3 ( 25 marks ) (a ) Astring oscillates according to the standing wave equation given below , * ( * , \$ ) = 0. 0 05 sin ( ( 30 + do)xx ) cos…

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Question Q3 ( 25 marks )(a ) Astring oscillates according to the standing wave equation given below ,* ( * , \$ ) = 0. 0 05 sin ( ( 30 + do)xx ) cos ( ( 40 – do )at )where * and yare in meters , and It is in seconds . Calculate the followings : -( 1) The amplitude and speed of the two transverse waves * 1 ( * , 1 ) and 1/ 2 ( * , I ) , identical buttravelling in opposite direction , whose superposition gives this * (* , * ) oscillation .14 marks )( 1) The distance between nodes of the standing wave .12 marks )lili ) The transverse speed of a particle of the string at the position * = 0. 015 m when t = 1.03 5 .1 4 marks !16 ) Two trains are travelling towards each other at 1 40 + del m/’s relative to the ground . One trainis blowing a whistle at (256 – 3 x dEl Hz . Given that the speed of sound through the air is 343m /’s , determine the followings : -lil The frequency heard on the other train in still air .15 marks )( in) The frequency heard on the other train if the wind is blowing at 30 m /’s towards the listener ,but away from the whistle .15 marks )lili ) The frequency heard if the wind direction of part ( 6 ) is reversed .15 marks )

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