Question

An aircraft travelling at 600 km/h accelerates steadily at 10 km/h per second. Taking the speed of sound as 1100 km/h at the aircraft's altitude, how long will it take to reach the 'sound barrier?

Answer 1

Hint: Sound is not electromagnetic and the speed of sound depends upon the nature of the medium in which it travels. The sound wave is a type of longitudinal wave.

Complete answer:
Sound wave is a type of longitudinal wave which means that it requires a medium to travel. When the longitudinal wave is produced the disturbance travels through the medium. As the medium is composed of many particles, these disturbances strike these and they move from one particle to another.
Given in the question:
The initial velocity of the aircraft i.e. u = 600 km/h
The final velocity the speed of sound i.e. v = 1100 km/h
And the acceleration is given as 10 km/h/s = 600$km/{{h}^{2}}$
Now we know the reaction between the final velocity, initial velocity, acceleration and time:
\[a=\dfrac{(v-u)}{t}\]
Where a = acceleration
v = final velocity
u= initial velocity
and t = time
Put all the given value in the above equation we get:
\[t=\dfrac{(v-u)}{a}=\dfrac{(1100-600)}{600}=\dfrac{5}{6}hr\]
= 50 second
Hence, it takes the aircraft 50 second to reach the sound barrier.

Note:
Sound is a wave which means that it spreads through the vibration of particles in a medium such as water or air. The vacuum is a space there is no medium for the sound to travel through it. The speed of the sound is determined by the dynamic movement of the sound waves. This depends on the characteristics of the medium through which the movement takes place.