Experiment Q2-1 Official(English)Acoustic blackbox1 A sound source is moving on a circle offixed radius R in x-y plane with a constant angular speed⑴.The circle is also moving with a uniform velocity Us which makes an angleβ(0o<β<90o)with the x-axis.Figure 1 shows the trajectory of the source in red color dash-dotted line.At time t=0,the center of the→circle is at C,with coordinates(XC,YC),the position of the source is given by vector CA from C.In addition,the source S starts moving anticlockwise(counterclockwise)direction(see Fig.1)simultaneously emitting→a sound of frequency f0 at time t=0.Vector CA makes an angleφwith respect to the x-axis at t=0(LBCA=φin Fig.1(a)).A detector D is kept in the same plane(x-y)such that its distance from the origin and the angle which the position vector makes with the x-axis are rD andθrespectively(in Fig.1(b)).Line joining the detector D and the source S makes an angleαwith the x-axis.All the motions of the source and the detector are in the x-y plane only.The speed of sound,c is 330m/s.Also,the net speed of the source is smaller than c.S A C D U s x y O(b)Trajectory of the source.rDθαA U sφC Bβ(a)Initial location of the source.y O x Figure 1 The sound emitted by the source is detected by the detector at time t with frequency f(t).The simulation displays the detected frequency f(t).0.2pt A.1 Obtain the equation of the trajectory(x(t),y(t))of the source in terms ofβ,φ,Us,and the other relevant quantities.
Click on"EQ2-Acoustic Black box"on the exam portal for the experimental exam.1 Siddharth Tiwary(IIT Powai,Mumbai),Siddhant Mukherjee(The University of Cambridge,UK),Chandan Relekar(IISc,Banga-lore),Charudutt Kadolkar(IIT Guwahati),Praveen Pathak(HBCSE-TIFR,Mumbai),were the principal authors of this problem.The contributions of the Academic Committee and the International Board are gratefully acknowledged.About simulation:There are two parts to the simulation.The upper part of the panel isthe input panel for the detector’s parameters and the lower part of the panel is the display of the graphical output of the frequency(f(t))detected by the detector at time t.Figure 2:Default simulation screen You can change the detector’s position by entering the values of rD andθin the input panel.If you change the value in the panel,you need to click the"PLOT GRAPH"to view the changed output of f(t).You can change the interval at which data is collected in thefield“Data-point intervalΔ”.Note that this interval can only be a multiple of 0.001s.You can set the detector in uniform motion by entering the speed ud and the angle 7,which velocity vector u(→)d makes with the x-axis.Again you have to click the"PLOT GRAPH"button to view the output for the changed parameters.Once the PLOT GRAPH button is clicked,a graph will be displayed for the interval"Graph Start time(ti)"to"Graph End time(tf)".In Fig.(2),the panel displays the graph for 0 to 25 s.Figure 3:Simulation screen for the changed input values Graph Start and End time input can also be used to zoom in on a portion of the graph.To illustrate,Fig.(3)shows the output for the case when the detector is placed at 5000 m at angle 78o.The graph output is plotted between 10-150 s.Data is collected at every 0.008 s.When you place the cursor over the curve’s data point,it shows the values of the data points.Since the time interval is very small,placing the cursor over the curve may show the values of multiple data points.In Fig.(3),eight data points are shown.Caution:If you keep the data point interval(Δ)very small(say 0.001)and plot it for a long time interval(say Graph Start time(ti=0)to Graph End time(tf=25s)),simulation will take a long time and may freeze depending on the capacity of your machine.If you are stuck in such a situation,follow the steps given in the General Instructions.Very smallΔcan be used only for a small time interval of the plot.While running simulation maximum number of data points that simulator can plot is 25000,irrespective of Graph End time(tf(s)).
""""""此处省略40%，请
登录会员，阅读正文所有内容。
