Question

Compare the time it

Answer 1

The sound takes about 874,000 times MORE time than the light takes.

Answer 2

Answer:

Light takes less time than sound.

Explanation:

Let's say, the teacher and the student are at a distance "d" from each other.

The medium around them would be air.

And,

The speed of light in air is approx. 3× 10⁸ m/s

while, the speed of sound in air is approx. 330 m/s

We have a formula that establishes the relation between speed, distance and time.

$\boxed{ \mathsf{speed = \frac{distance}{time} }}$

Our hunt for time — Speed in both the scenarios is known to us whereas the distance is same.

Sound

$\mathsf{330 = \frac{d}{time_{s}} }$

$\underline{\mathsf{time _{s} = \frac{d}{330} }}$

Light

$\mathsf{3 \times {10}^{8} = \frac{d}{time _{l} } }$

$\underline{ \mathsf{ time _{l} = \frac{d}{3 \times {10}^{8}} }}$

The best way of comparison is finding their ratio.

$\implies \mathsf{\frac{ time_{s}}{time_{l} } = \frac{ \frac{d}{330} }{ \frac{d}{3 \times {10}^{8} } } }$

simplifying the fraction

$\implies \mathsf{\frac{ time_{s}}{time_{l} } = \frac{d \times (3 \times {10}^{8} )}{330 \times d}}$

d gets canceled and we're left with the following expression

$\implies \mathsf{\frac{ time_{s}}{time_{l} } = \frac{ (3 \times10 \times {10}^{7} )}{330}}$

30, being a common factor in the numerator as well as denominator, gets canceled out. and in its place remains 1/ 11

(why?

=> 30÷330 = 1÷11)

$\implies \mathsf{\frac{ time_{s}}{time_{l} } = \frac{ 1\times {10}^{7} }{11}}$

taking timeₛ to the numerator on the other side.

$\implies \mathsf{time_{s} = \frac{ 1\times {10}^{7} }{11}\times time_{l}}$

Therefore, we get timeₛ is approx. 10⁶ times the timeₗ.

That's a big difference, no wonder light's way much faster than sound.

As lesser the time taken to cover a distance, faster is the wave.