Sound. Echo

Sound as a mechanical wave, pitch and loudness, the speed of sound in different media, echo and finding the distance to a barrier.

Terms

Studied 0 of 4

Formulas

Distance to a barrier from the echo

s = \dfrac{v\,t}{2}

Quantities
Symbol	Name	Unit
$s$	distance to the barrier	m
$v$	speed of sound in the medium	m/s
$t$	time from the sound to the return of the echo	s

Solved for another quantity:

v = \dfrac{2s}{t}

t = \dfrac{2s}{v}

Note. The sound covers the path $2s$ (to the barrier and back) with a constant speed: $2s = vt$ . Example: the echo returned after $t = 2\ \text{s}$ , $v = 340\ \text{m/s}$ , so $s = \dfrac{340 \cdot 2}{2} = 340\ \text{m}$ .

Lab

Set the quantities with the sliders. The graphs and the formulas with your numbers update at once.

Sound and echo

The blue pulse is the sound going to the barrier, the red one is the reflected sound coming back. The distance to the barrier is not to scale. The show always lasts a few seconds while the real time until the echo is given by the slider and in the calculation.

t

= 0 s

Graphs

The distance of the sound from the source: it first grows up to the distance to the barrier and then falls to zero. Click the graph to move through it.

s(t)

v

340 m/s

s

170 m

t

1 s

Echoheard separately

Formulas with your numbers

t = \dfrac{2s}{v} = \dfrac{2 \cdot 170}{340} = 1\ \text{s}

s = \dfrac{vt}{2} = \dfrac{340 \cdot 1}{2} = 170\ \text{m}

The ear tells sounds apart if they are at least 0.1 s apart (in air this means a barrier at least 17 m away).

How to read the graphs

The $s(t)$ graph shows the distance of the sound from the source: first a straight line going up (the sound travels to the barrier with the speed $v$ ), then a straight line going down (the reflected sound comes back).
The peak of the graph is the moment the sound reaches the barrier. It is half of the time until the echo, and the height of the peak is the distance $s$ to the barrier.
The moment the graph returns to zero is the time $t$ until the echo. The sound has covered the path $2s$ there and back, so $2s = vt$ and $s = \dfrac{vt}{2}$ .
The greater the speed of sound in the medium, the steeper the lines of the graph and the shorter the time until the echo for the same distance.

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Terms

Studied 0 of 4

Formulas

Distance to a barrier from the echo

s = \dfrac{v\,t}{2}

Quantities
Symbol	Name	Unit
$s$	distance to the barrier	m
$v$	speed of sound in the medium	m/s
$t$	time from the sound to the return of the echo	s

Solved for another quantity:

v = \dfrac{2s}{t}

t = \dfrac{2s}{v}

Lab

Set the quantities with the sliders. The graphs and the formulas with your numbers update at once.

Sound and echo

t

= 0 s

Graphs

The distance of the sound from the source: it first grows up to the distance to the barrier and then falls to zero. Click the graph to move through it.

s(t)

v

340 m/s

s

170 m

t

1 s

Echoheard separately

Formulas with your numbers

t = \dfrac{2s}{v} = \dfrac{2 \cdot 170}{340} = 1\ \text{s}

s = \dfrac{vt}{2} = \dfrac{340 \cdot 1}{2} = 170\ \text{m}

The ear tells sounds apart if they are at least 0.1 s apart (in air this means a barrier at least 17 m away).

How to read the graphs

The

s(t)

graph shows the distance of the sound from the source: first a straight line going up (the sound travels to the barrier with the speed

v

), then a straight line going down (the reflected sound comes back).

The peak of the graph is the moment the sound reaches the barrier. It is half of the time until the echo, and the height of the peak is the distance

s

to the barrier.

The moment the graph returns to zero is the time

t

until the echo. The sound has covered the path

2s

there and back, so

2s = vt

and

s = \dfrac{vt}{2}

The greater the speed of sound in the medium, the steeper the lines of the graph and the shorter the time until the echo for the same distance.