What is the time interval between two sounds heard by an observer standing on a railway line 2 km away when a detonator is exploded on the line made of steel?
The time interval between these two sounds is 0.0039 s.
Calculating Time Interval
The time interval between the two sounds that an observer standing on the rail 2 km away hears when a detonator is exploded on a railway line made of steel can be calculated using the speed of sound in steel and the distance between the observer and the detonator.
Speed of Sound in Steel:
The speed of sound in a material is given by the formula:
v = (E/p)^0.5
where v is the speed of sound, E is the Young's modulus of the material, and p is the density of the material.
Plugging in the values given in the question:
v = (2 x 10^11 nm^-2 / 8000 kg/m^3)^0.5
v = 5103 m/s
Calculating Time Interval:
The time interval between the two sounds can be calculated using the formula:
t = d/v
where t is the time interval, d is the distance between the observer and the detonator, and v is the speed of sound.
Plugging in the values given in the question:
t = 2 km / 5103 m/s
t = 0.0039 s
Therefore, the time interval between the two sounds that the observer hears is approximately 0.0039 seconds.