2008 Semifinal Exam Part A 6 Question A4 A tape recorder playing a single tone of frequency fo is dropped from rest at a height h.You stand directly underneath the tape recorder and measure the frequency observed as a function of time.Here t=0s is the time at which the tape recorder was dropped. t (s)f (Hz) 2.0 581 4.0 619 6.0 665 8.0 723 10.0 801 The acceleration due to gravity is g=9.80 m/s2 and the speed of sound in air is vsnd =340 m/s.Ignore air resistance.You might need to use the Doppler shift formula for co-linear motion of sources and observers in still air, f=snd土obs Usnd士Usrd where fo is the emitted frequency as determined by the source,f is the frequency as detected by the observer, and Usnd,Usre,and vobs are the speed of sound in air,the speed of the source,and the speed of the observer. The positive and negative signs are dependent upon the relative directions of the motions of the source and the observer. a.Determine the frequency measured on the ground at time t,in terms of fo,g,h,and vsnd.Consider only the case where the falling tape recorder doesn't exceed the speed of sound Usnd. b.Verify graphically that your result is consistent with the provided data. c.What (numerically)is the frequency played by the tape recorder? d.From what height h was the tape recorder dropped? Copyright C2008 American Association of Physics Teachers2008 Semifinal Exam Part A 6 Question A4 A tape recorder playing a single tone of frequency f0 is dropped from rest at a height h. You stand directly underneath the tape recorder and measure the frequency observed as a function of time. Here t = 0 s is the time at which the tape recorder was dropped. t (s) f (Hz) 2.0 581 4.0 619 6.0 665 8.0 723 10.0 801 The acceleration due to gravity is g = 9.80 m/s 2 and the speed of sound in air is vsnd = 340 m/s. Ignore air resistance. You might need to use the Doppler shift formula for co-linear motion of sources and observers in still air, f = f0 vsnd ± vobs vsnd ± vsrc where f0 is the emitted frequency as determined by the source, f is the frequency as detected by the observer, and vsnd, vsrc, and vobs are the speed of sound in air, the speed of the source, and the speed of the observer. The positive and negative signs are dependent upon the relative directions of the motions of the source and the observer. a. Determine the frequency measured on the ground at time t, in terms of f0, g, h, and vsnd. Consider only the case where the falling tape recorder doesn’t exceed the speed of sound vsnd. b. Verify graphically that your result is consistent with the provided data. c. What (numerically) is the frequency played by the tape recorder? d. From what height h was the tape recorder dropped? Copyright c 2008 American Association of Physics Teachers