At standard temperature and pressure sound travels at speed

At standard temperature and pressure sound travels at speed vs = 330 m/s relative to the air through which it propagates. Four students, A, B, C, D, position themselves as shown in the ?gure, with A, B, C in a straight line and D vertically above B. A steady wind is blowing with speed v = 30 m/s along the line ABC. If B ?res a revolver, what are the speeds with which the sound will travel to A, C, and D (in the reference frame of the observers)? Discuss whether the di?erences in your answers could be detected.

Solution

If B fire a revolver the speed of the sound towards A is reduced because of the wind blowing in opposite direction

the speed of sound towards A is = 330m/sec - 30 m/s = 300 m/sec

and the speed of sound from B to C wil get increased = 330 + 30 = 360m/s   (since the wind and sound are in same direction)

and the speed of sound from B to D will not change it will remian the same = 330 m/s

since the direction of sound towards B is not facing towards or aganist wind direction

The differences in the sound speed from B towards A or from B towards C are not detectable.

untill the speration between them is greater than 600 m or more

since the speed difference is 30 m/s on either side with wind and with out wind

the time difference is = time = 30 / 330 = 0.09^th of a second is the time delay with wind and with out wind

which is not detectable time difference for human ears.