Saved Bookmarks
| 1. |
An engine whistling at a constant frequency and moving with a constant velocity goes past a stationary observer. As the engine crosses him, the frequency of the sound heard by him changes by a factor f. The actual difference in the frequencies of sound heard by him before and after the engine crosses him is |
|
Answer» nd of frequency N heard by a stationary observer from a SOURCE of sound moving with velocity Vs towards the observer is given by, ν'=VnV−Vs−−−(1)and when source of sound MOVES away from the observer then, ν''=VnV+Vs−−−(2) But we are given, ν'−V''=f=Vn(1V−Vs−1V+Vs)=−2V n Vs(V2−Vs2)or f = −2n ×VVs[(VVs)2−1]−−−−(3)again ν'=VnV−Vs= fVnV+Vsor f(V−Vs)=V+Vsor V(f−1)=Vs(1+f)or VVs=1+ff−1−−−(4)Now putting the value of VVs from eqn (4) in eqn (3), we get, ν'=−2n×1+ff−1[(1+ff−1)2−1]=2n×(1−f2)4f=n×(1−f2)2f. proved. |
|