Question

A soldier sets his watch on hearing a distant siren. His watch will record:
A) Less than actual time
B) More than actual time
C) Perfectly correct time
D) Nothing can be said

Answer 1

Hint: We know the travelling speed of the sound is three hundred and forty four metres per second. This means that sound will travel three hundred and forty four metres in one second. Thus, it gives a hint that the sound of the siren is going to reach the soldier after some time. This gives us a solid hint for the answer of this question.

Complete step by step solution:
The speed of the sound is three hundred and forty four metres in one second. The siren is located very far or distant as given in the question. This means if we assume that, distance between the soldier and the siren is one thousand metres then sound will be taking around three seconds to reach the soldier.
The calculation of the time can be done by using the formula.
$\Rightarrow \text{speed}={\displaystyle \frac{\text{distance}}{\text{time}}}$
Mathematically, it is written in the form as,
$\Rightarrow v={\displaystyle \frac{s}{t}}$
Where,
$v$ = speed of the sound
$s$ = distance travelled by the sound
$t$ = time taken by the sound to cover the distance
Putting the value in the equation, we get
$\Rightarrow v={\displaystyle \frac{s}{t}}$
$\Rightarrow 344={\displaystyle \frac{1000}{t}}$
$\Rightarrow t={\displaystyle \frac{1000}{344}}$
$\Rightarrow t=2.90s$
So, approximately three seconds will be taken by the sound to reach the soldier from the siren.
Hence, if the soldier is going to set his watch after hearing the sound of the siren, then he is going to set his watch three seconds later or we can say, his watch is delayed by three seconds. Also, it can be interpreted in this manner, the soldier’s watch has less than the actual time.

Thus, option (A) is the correct answer.

Note: The siren is located far away from the soldier and the soldier will set his watch after he hears the sound so the delay that the sound will have to reach soldier from the siren soldier and also the delay as the soldier will take some time to set the watch because of the human response delay.