Frequency help!!!!!!

Question

my physics book(glencoe's physics: principles and problems) does a horrible job explaining teaching these kind of problems...can some explain this???

The following is the equation for the Doppler shift of a sound wave of speed v reaching a moving detector.

fd = fs(v vd)/(v - vs)

In this equation, vd is the speed of the detector, and vs is the speed of the source. Also, fs is the frequency of the source, and fd is the frequency of the detector. If the detector moves toward the source, vd is positive. If the source moves toward the detector, vs is positive. A train moving toward a detector at 30 m/s blows a 305 Hz horn.

(a) What frequency is detected by a stationary train?

___ Hz

(b) What frequency is detected by a train moving toward the first train at 21 m/s?

___ Hz

Answer 1

fd = fs(v + vd)/(v - vs)

a): here vd=0, vs=30 m/s ,fs=305Hz

we take speed of sound v =340m/s

then:

fd=305(340)/(340-30)

=305*340/310

=334.516129 Hz

(b):

vd=21m/s

then

fd=305(340+21)/(340-30)

=355.17742Hz

if source and detector move towards each other take vd positive and vs negative

if they move away then take vd negative and vs positive