Question

A man is standing between two vertical walls 680 m apart. He claps his hands and hearts two distinct echoes after 0.9 seconds and 1.1 second respectively. What is the speed of sound in the air

Answer 1

Answer:

Let speed of sound be v

$\frac{2x}{v} = 0.9 \\ \frac{2(680 - x)}{v} = 1.1 \\ 1.1v = 1360 - 2x = 1360 - 0.9v \\ 2v = 1360 \\ v = 680 \frac{m}{s}$

Answer 2

The speed of sound in air is 441.93 m/s.

Explanation:

Given that,

Distance = 680 m

let the man is at a distance x from the first cliff and then he is at ( 685 - x) m from second cliff .

Now look the distance traveled by the wave to reach the man in 0.9 second will have to travel 2 x distance from first cliff and also true for second cliff .

We need to calculate the velocity

Using formula of distance

$v=\dfrac{d}{t}$

$v=\dfrac{2x}{0.9}$....(I)

$v=\dfrac{(685-x)}{1.1}$....(II)

From equation (I) and (II)

$\dfrac{2x}{0.9}=\dfrac{(685-x)}{1.1}$

$2.2x+0.9x=685\times0.9$

$3.1x=616.5$

$x=\dfrac{616.5}{3.1}$

$x=198.87\ m$

We need to calculate the speed of sound in air

Using equation (I)

$v=\dfrac{2x}{0.9}$

Put the value into the formula

$v=\dfrac{2\times198.87}{0.9}$

$v=441.93\ m/s$

Hence, The speed of sound in air is 441.93 m/s.

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Topic : speed of sound

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