---
title: "Sound: Production and Propagation"
book: "Primary & Middle School Physics"
subject: physics
language: en
chapter: 53
exercises: 12
source: https://one-course.com/books/physics/1/en/chapter/53-sound-production-and-propagation
---

# Chapter 53 — Sound: Production and Propagation

You have known since childhood that [sound](https://one-course.com/books/physics/1/en/chapter/19-sound-around-us#def-g3-sound-around-us-sound) is born in a trembling and dies in emptiness — the rice grains danced, the bell in the jar fell silent. What you lacked was the messenger’s name. Now you own the molecular world, and [sound](https://one-course.com/books/physics/1/en/chapter/19-sound-around-us#def-g3-sound-around-us-sound)’s whole journey — from a guitar string to your eardrum, through [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air), water or steel — can finally be watched from inside.

## 53.1 The messengers

**Definition 53.1 (Medium).**

A *medium* (plural *media*) is the substance a [sound](https://one-course.com/books/physics/1/en/chapter/19-sound-around-us#def-g3-sound-around-us-sound) travels through: [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air), water, wood, steel — any state will serve, for all are crowds of [molecules](https://one-course.com/books/physics/1/en/chapter/45-states-of-matter-and-changes-of-state#def-g7-states-of-matter-molecule). What no [sound](https://one-course.com/books/physics/1/en/chapter/19-sound-around-us#def-g3-sound-around-us-sound) can cross is the absence of a crowd: vacuum, the empty stage.

**Proposition 53.2 (How sound travels).**

A vibrating source shoves the [molecules](https://one-course.com/books/physics/1/en/chapter/45-states-of-matter-and-changes-of-state#def-g7-states-of-matter-molecule) beside it; they crowd against their neighbors and rebound; the neighbors shove the next rank in turn. The shove — a traveling squeeze of the crowd — races outward from the source in every direction, [molecule](https://one-course.com/books/physics/1/en/chapter/45-states-of-matter-and-changes-of-state#def-g7-states-of-matter-molecule) relaying [molecule](https://one-course.com/books/physics/1/en/chapter/45-states-of-matter-and-changes-of-state#def-g7-states-of-matter-molecule), though each [molecule](https://one-course.com/books/physics/1/en/chapter/45-states-of-matter-and-changes-of-state#def-g7-states-of-matter-molecule) itself only jiggles about its place. [Sound](https://one-course.com/books/physics/1/en/chapter/19-sound-around-us#def-g3-sound-around-us-sound) is the *relay*, not the runners: the message travels; the messengers stay home.

![Sound inside the air: the source’s shove travels as a relay of squeezes through the molecular crowd — each molecule jiggling in place, the pattern racing on.](https://one-course.com/images/onecourse/chapters/physics-1/g7-sound-production/fig-a24881db9ae1.svg)

*[Sound](https://one-course.com/books/physics/1/en/chapter/19-sound-around-us#def-g3-sound-around-us-sound) inside the [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air): the source’s shove travels as a relay of squeezes through the molecular crowd — each [molecule](https://one-course.com/books/physics/1/en/chapter/45-states-of-matter-and-changes-of-state#def-g7-states-of-matter-molecule) jiggling in place, the pattern racing on.*

**Example 53.3 (The jar, explained at last).**

The famous silenced bell now confesses its mechanism. Pumping out the [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) removes the crowd: the bell’s trembling walls shove at nothing, no relay forms, and no message crosses the glass. The bell never stopped — it lost its messengers. And space’s great silence follows at once: between the [stars](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-star) there is no crowd to carry a cry.

**Example 53.4 (Loud, quiet, and worn out).**

A harder shove makes a stronger squeeze: louder [sound](https://one-course.com/books/physics/1/en/chapter/19-sound-around-us#def-g3-sound-around-us-sound). And as the relay spreads — pond-rings in three dimensions — each squeeze is shared over a vaster and vaster shell of crowd, weakening with distance: why shouts fade, and why the neighbor’s music is a murmur through two walls. Nothing of this needed new laws: crowd physics pays for everything.

![A plucked string photographed mid-song: the vibration blurs it into a wide band, widest at the middle, still at its two fixed ends.](https://one-course.com/images/onecourse/chapters/physics-1/g7-sound-production/img-9ce0cd788564.jpg)

*A plucked string photographed mid-song: the [vibration](https://one-course.com/books/physics/1/en/chapter/19-sound-around-us#def-g3-sound-around-us-vibration) blurs it into a wide band, widest at the middle, still at its two fixed ends.*

## 53.2 Every medium has its pace

**Proposition 53.5 (The speed of sound depends on the medium).**

The relay’s [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) is a property of the crowd:

1. in [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) : about $340\,\mathrm{m}/\mathrm{s}$ ;
2. in water: about $1500\,\mathrm{m}/\mathrm{s}$ — four times faster;
3. in steel: about $5000\,\mathrm{m}/\mathrm{s}$ — fifteen times faster than [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) .

The pattern: the more tightly a [medium](#def-g7-sound-production-medium)’s [molecules](https://one-course.com/books/physics/1/en/chapter/45-states-of-matter-and-changes-of-state#def-g7-states-of-matter-molecule) touch, the faster they hand the shove along. Flying [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) [molecules](https://one-course.com/books/physics/1/en/chapter/45-states-of-matter-and-changes-of-state#def-g7-states-of-matter-molecule) must first cross gaps to deliver; water’s touching crowd relays briskly; steel’s locked ranks pass the message almost hand-to-hand.

![Three crowds, three paces: the tighter the molecules’ contact, the faster the relay.](https://one-course.com/images/onecourse/chapters/physics-1/g7-sound-production/fig-1484726859e6.svg)

*Three crowds, three paces: the tighter the [molecules](https://one-course.com/books/physics/1/en/chapter/45-states-of-matter-and-changes-of-state#def-g7-states-of-matter-molecule)’ contact, the faster the relay.*

**Example 53.6 (Old scenes, new numbers).**

The scout’s ear on the rail: the steel relay outruns the [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air)’s by a factor of fifteen — the rail’s warning arrives long before the rumble. Whales’ songs crossing seas: water’s swift, generous relay. And your own voice [sounds](https://one-course.com/books/physics/1/en/chapter/19-sound-around-us#def-g3-sound-around-us-sound) strange on recordings partly because, speaking, you hear yourself through the skull’s bone-relay as well as through [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) — two media, two versions, and only other people ever hear the air-only one.

## 53.3 Sound with a stopwatch

**Method 53.7 (Measuring the speed of sound).**

The oldest method still works on any sports field:

1. a partner stands a measured $680\,\mathrm{m}$ away (two field-lengths and a bit — pace it or use the field’s markings) with two pan lids;
2. they clash the lids overhead: you *see* the strike instantly ( [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) ’s trip is as good as instant), and start the stopwatch on the flash of motion;
3. stop on the arriving clang: expect very nearly $2\,\mathrm{s}$ ;
4. compute: $v = d/t = 680 \div 2 = 340\,\mathrm{m}/\mathrm{s}$ .

Repeat and average — reaction times scatter, as the honest measurement chapter taught. Thunder-counting is this method run backward: knowing $v$, the silent seconds hand you the distance.

**Example 53.8 (The echo, computed).**

A clap toward a cliff returns in $3\,\mathrm{s}$. The [sound](https://one-course.com/books/physics/1/en/chapter/19-sound-around-us#def-g3-sound-around-us-sound) traveled to the cliff and back: $d_{\text{round trip}} = 340 \times 3 =
1020\,\mathrm{m}$, so the cliff stands at half: $510\,\mathrm{m}$. The rule of every [echo](https://one-course.com/books/physics/1/en/chapter/27-how-sound-travels#ex-g4-how-sound-travels-echo) sum: the measured time pays for the round trip — forgetting the “and back” is the classic slip, and doubles every answer wrongly.

**Example 53.9 (Sonar, in earnest).**

The survey ship’s sonar clicks downward; the seabed’s [echo](https://one-course.com/books/physics/1/en/chapter/27-how-sound-travels#ex-g4-how-sound-travels-echo) returns in $0.6\,\mathrm{s}$. In *water*, $d = 1500 \times 0.6 =
900\,\mathrm{m}$ round trip: depth $450\,\mathrm{m}$. Dolphins and bats run the same arithmetic by instinct; ships print it on charts. Note the discipline: the [medium](#def-g7-sound-production-medium) chooses the [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) — feeding an underwater [echo](https://one-course.com/books/physics/1/en/chapter/27-how-sound-travels#ex-g4-how-sound-travels-echo) the [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air)’s $340$ is the chapter’s second classic slip.

**Remark 53.10 (What “fast” still is not).**

Steel’s $5000\,\mathrm{m}/\mathrm{s}$ [sounds](https://one-course.com/books/physics/1/en/chapter/19-sound-around-us#def-g3-sound-around-us-sound) heroic — until [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) is recalled. In the storm, the flash’s trip counts as instant while thunder jogs its kilometre in three seconds; and no [medium](#def-g7-sound-production-medium), not steel, not diamond, brings [sound](https://one-course.com/books/physics/1/en/chapter/19-sound-around-us#def-g3-sound-around-us-sound) within shouting distance of [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)’s pace. Exactly how fast [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) runs — and how humans finally clocked something that crosses a room in a hundred-millionth of a second — is next year’s story, with a chapter of its own.

## 53.4 Exercises

**Exercise 53.1 ★.**

What is a [medium](#def-g7-sound-production-medium)? Name three, and the one “[non-medium](#def-g7-sound-production-medium)” no [sound](https://one-course.com/books/physics/1/en/chapter/19-sound-around-us#def-g3-sound-around-us-sound) can cross.

**Solution of Exercise 53.1.**

The substance a [sound](https://one-course.com/books/physics/1/en/chapter/19-sound-around-us#def-g3-sound-around-us-sound) travels through — [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air), water, wood, steel, any molecular crowd. The [non-medium](#def-g7-sound-production-medium): vacuum.

**Exercise 53.2 ★.**

In the relay picture, what travels from source to ear — and what does each individual [molecule](https://one-course.com/books/physics/1/en/chapter/45-states-of-matter-and-changes-of-state#def-g7-states-of-matter-molecule) do?

**Solution of Exercise 53.2.**

The relay travels: a racing pattern of squeezes handed from rank to rank of the crowd. Each [molecule](https://one-course.com/books/physics/1/en/chapter/45-states-of-matter-and-changes-of-state#def-g7-states-of-matter-molecule) only jiggles about its home place — the message moves, the messengers stay.

**Exercise 53.3 ★.**

Explain the silenced bell-in-the-jar with [molecules](https://one-course.com/books/physics/1/en/chapter/45-states-of-matter-and-changes-of-state#def-g7-states-of-matter-molecule) — and why films’ roaring space battles are physics fiction.

**Solution of Exercise 53.3.**

No crowd, no relay: the pumped-out jar leaves the bell’s trembling walls shoving at nothing, so no message forms. Space battles are silent for the same reason — explosions between the [stars](https://one-course.com/books/physics/1/en/chapter/26-the-solar-system#def-g4-solar-system-star) have no crowd to carry their roar.

**Exercise 53.4 ★.**

Give the three [speeds](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) of the chapter’s table, and the pattern connecting a [medium](#def-g7-sound-production-medium)’s molecular arrangement to its pace.

**Solution of Exercise 53.4.**

[Air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) about $340\,\mathrm{m}/\mathrm{s}$; water about $1500\,\mathrm{m}/\mathrm{s}$; steel about $5000\,\mathrm{m}/\mathrm{s}$. The tighter the [molecules](https://one-course.com/books/physics/1/en/chapter/45-states-of-matter-and-changes-of-state#def-g7-states-of-matter-molecule) touch, the faster the shove is handed on: flying, touching, locked.

**Exercise 53.5 ★.**

Why does the scout’s rail-message outrun the [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air)’s? By roughly what factor?

**Solution of Exercise 53.5.**

Steel’s locked ranks relay nearly hand-to-hand: about fifteen times the [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air)’s pace, so the rail’s message arrives long before the airborne rumble.

**Exercise 53.6 ★.**

In the field measurement, why is watching the lids’ strike as good as a starting gun at the source itself?

**Solution of Exercise 53.6.**

[Light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)’s trip across any field counts as instant beside [sound](https://one-course.com/books/physics/1/en/chapter/19-sound-around-us#def-g3-sound-around-us-sound)’s: the seen strike marks the true start to far better precision than the stopwatch hand can use.

**Exercise 53.7 ★.**

A clap’s [echo](https://one-course.com/books/physics/1/en/chapter/27-how-sound-travels#ex-g4-how-sound-travels-echo) from a warehouse wall returns in $1\,\mathrm{s}$. How far is the wall? Name the slip that would answer $340\,\mathrm{m}$.

**Solution of Exercise 53.7.**

$340 \times 1 = 340\,\mathrm{m}$ round trip: the wall stands at $170\,\mathrm{m}$. Answering $340\,\mathrm{m}$ forgets that the second paid for going *and* coming back.

**Exercise 53.8 ★.**

A ship’s sonar [echo](https://one-course.com/books/physics/1/en/chapter/27-how-sound-travels#ex-g4-how-sound-travels-echo) returns in $2\,\mathrm{s}$. The depth? Name the slip that would use $340\,\mathrm{m}/\mathrm{s}$.

**Solution of Exercise 53.8.**

In water: $1500 \times 2 = 3000\,\mathrm{m}$ round trip — depth $1500\,\mathrm{m}$. The slip: borrowing the [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air)’s $340\,\mathrm{m}/\mathrm{s}$ for an underwater journey.

**Exercise 53.9 ★★.**

Fireworks over the bay: you see the burst, and hear it $2.5\,\mathrm{s}$ later. How far is the shell? Why is the same computation useless for judging the distance of a *jet* you can hear but not see?

**Solution of Exercise 53.9.**

$d = 340 \times 2.5 = 850\,\mathrm{m}$. The firework’s flash gave a true starting gun; the unseen jet offers none — no moment of emission to time from — and worse, the heard roar left the jet seconds ago: the ear points at where the jet *was*.

**Exercise 53.10 ★★.**

A swimmer with one ear underwater hears the pool’s underwater speaker before a friend on the deck hears it through [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) — though the friend stands nearer. Reconcile with the table.

**Solution of Exercise 53.10.**

The underwater ear is served by water’s $1500\,\mathrm{m}/\mathrm{s}$ relay, the deck ear by [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air)’s $340\,\mathrm{m}/\mathrm{s}$ — and much of the speaker’s [sound](https://one-course.com/books/physics/1/en/chapter/19-sound-around-us#def-g3-sound-around-us-sound) never crosses the surface border into the [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) at all. Faster [medium](#def-g7-sound-production-medium), private message: the swimmer wins despite the distance.

**Exercise 53.11 ★★.**

Old railway lore: put your ear to the rail and you hear the train *twice*. Explain the two arrivals, and compute the gap for a train $3\,\mathrm{km}$ away (steel at $5000\,\mathrm{m}/\mathrm{s}$, [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) at $340\,\mathrm{m}/\mathrm{s}$ — one decimal is enough).

**Solution of Exercise 53.11.**

One blow, two relays: through steel and through [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air). Steel: $3000 \div 5000 = 0.6\,\mathrm{s}$; [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air): $3000 \div 340 \approx
8.8\,\mathrm{s}$ — the clang leads the boom by about $8.2\,\mathrm{s}$.

**Exercise 53.12 ★★★.**

Design a measurement of the [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) of [sound](https://one-course.com/books/physics/1/en/chapter/19-sound-around-us#def-g3-sound-around-us-sound) *in water* for a calm lake, using a waterproof clacker, a hydrophone (an underwater microphone) $750\,\mathrm{m}$ away, and a recorder that also captures the clacker’s airborne clap through a normal microphone beside it. Explain how comparing the two recorded arrival times yields water’s [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) — and compute the expected gap between the two arrivals.

**Solution of Exercise 53.12.**

One clack sends the same instant into both media; at $750\,\mathrm{m}$ the recorder captures the water arrival (on the hydrophone) and the [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) arrival (on the microphone). Expected times: water $750 \div 1500 = 0.5\,\mathrm{s}$, [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) $750 \div 340
\approx 2.2\,\mathrm{s}$ — a gap of about $1.7\,\mathrm{s}$. Run backward: with $d$ and the [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) known, the measured gap gives the water arrival time ($t_{\text{air}} -
\text{gap}$), and $v = 750 \div 0.5 = 1500\,\mathrm{m}/\mathrm{s}$ — water’s pace measured without ever timing the silent clack itself.

## 53.5 Problem: The Canyon Survey

**Problem 53.1.**

Weekend problem — mapping the silent canyon by ear; echoes, rails and river depths; the surveyor’s toolkit

A survey team maps a remote canyon with stopwatches, one sonar [unit](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring), and the physics of this chapter. [Speeds](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula): [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) $340\,\mathrm{m}/\mathrm{s}$, water $1500\,\mathrm{m}/\mathrm{s}$, steel $5000\,\mathrm{m}/\mathrm{s}$.

**Part I — Widths by [echo](https://one-course.com/books/physics/1/en/chapter/27-how-sound-travels#ex-g4-how-sound-travels-echo).**

1. From the eastern rim, a clap’s [echo](https://one-course.com/books/physics/1/en/chapter/27-how-sound-travels#ex-g4-how-sound-travels-echo) off the western wall returns in $4\,\mathrm{s}$ . How wide is the canyon here?
2. At a narrower point, the [echo](https://one-course.com/books/physics/1/en/chapter/27-how-sound-travels#ex-g4-how-sound-travels-echo) returns in $1.5\,\mathrm{s}$ . The width?
3. A surveyor standing *between* two parallel walls claps once and hears two distinct [echoes](https://one-course.com/books/physics/1/en/chapter/27-how-sound-travels#ex-g4-how-sound-travels-echo) : after $1\,\mathrm{s}$ and after $2\,\mathrm{s}$ . How far is each wall, and how wide is the canyon on this line?
4. Why does the biggest measurement error in Part I come from the stopwatch hand, not the formula? (Cite the wisdom of the repeated-measurement rule.)

**Part II — The river below.**

5. The sonar [unit](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) , floated on the river, pings the bottom: [echo](https://one-course.com/books/physics/1/en/chapter/27-how-sound-travels#ex-g4-how-sound-travels-echo) in $0.2\,\mathrm{s}$ . The river’s depth?
6. The same [unit](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) pinged sideways toward a submerged boulder returns an [echo](https://one-course.com/books/physics/1/en/chapter/27-how-sound-travels#ex-g4-how-sound-travels-echo) in $0.4\,\mathrm{s}$ . Distance to the boulder?
7. A teammate suggests saving batteries: “shout from the boat and time the bottom [echo](https://one-course.com/books/physics/1/en/chapter/27-how-sound-travels#ex-g4-how-sound-travels-echo) by ear.” Two physical reasons this fails where the sonar succeeds. (Think of the border between media, and of what a shout’s [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) relay must do at the surface.)
8. The riverbed drops sharply mid-channel: predict what the sonar’s [echo](https://one-course.com/books/physics/1/en/chapter/27-how-sound-travels#ex-g4-how-sound-travels-echo) time does as the boat drifts across the drop.

**Part III — The old mining rail.** A straight abandoned rail runs $2\,\mathrm{km}$ along the canyon floor to the mine gate.

9. A hammer blow on the rail at the gate: compute the two arrival times at the surveyors’ end — through steel, and through [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) .
10. The team hears rail-clang and air-boom separated by that gap. Explain how the *gap alone* could [measure](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) the distance to the gate if the $2\,\mathrm{km}$ were unknown (describe the reasoning; the computation is Part III’s gift to the keen).
11. Fog fills the canyon overnight — useless for lamps and [mirrors](https://one-course.com/books/physics/1/en/chapter/32-mirrors-and-reflection#def-g5-mirrors-reflection-reflection) . Which of the team’s three measuring channels ( [air-sound](https://one-course.com/books/physics/1/en/chapter/19-sound-around-us#def-g3-sound-around-us-sound) , [water-sound](https://one-course.com/books/physics/1/en/chapter/19-sound-around-us#def-g3-sound-around-us-sound) , [rail-sound](https://one-course.com/books/physics/1/en/chapter/19-sound-around-us#def-g3-sound-around-us-sound) ) does fog disturb least, and why?
12. Write the surveyor’s log: three sentences — the round-trip rule, the medium-chooses-the-speed rule, and which single instrument (eye or ear) started every timing in the canyon, and why it may be trusted as “instant”.

**Solution of Problem 53.1.**

**1.** $340 \times 4 = 1360\,\mathrm{m}$ round trip: width $680\,\mathrm{m}$. **2.** $340 \times 1.5 = 510$; half: $255\,\mathrm{m}$. **3.** First wall: $340 \times 1 \div 2 = 170\,\mathrm{m}$; second: $340 \times 2 \div 2 = 340\,\mathrm{m}$; the canyon spans $170 + 340 = 510\,\mathrm{m}$ along that line. **4.** The formula is exact; the hand is not: human starting and stopping scatters by tenths of a second — tens of [metres](https://one-course.com/books/physics/1/en/chapter/7-measuring-length#def-g2-measuring-length-units) at $340\,\mathrm{m}/\mathrm{s}$. Hence the old rule: repeat, watch the readings huddle, report the huddle. **5.** $1500 \times 0.2 = 300\,\mathrm{m}$ round trip: depth $150\,\mathrm{m}$. **6.** $1500 \times 0.4 \div 2 = 300\,\mathrm{m}$. **7.** At the air–water border most of a shout is turned back — little enters the river, and the weak bottom [echo](https://one-course.com/books/physics/1/en/chapter/27-how-sound-travels#ex-g4-how-sound-travels-echo) must cross the border again to reach an ear in [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air): almost nothing survives. And even granting the [echo](https://one-course.com/books/physics/1/en/chapter/27-how-sound-travels#ex-g4-how-sound-travels-echo), round trips of tenths of a second defeat any by-ear timing. **8.** The [echo](https://one-course.com/books/physics/1/en/chapter/27-how-sound-travels#ex-g4-how-sound-travels-echo) time lengthens abruptly as the boat crosses the drop — deeper bottom, longer round trip: the sonar draws the cliff underwater. **9.** Steel: $2000 \div 5000 = 0.4\,\mathrm{s}$; [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air): $2000
\div 340 \approx 5.9\,\mathrm{s}$. **10.** Both relays start together, so the gap grows in proportion to the distance: each kilometre adds a fixed extra delay to the slow relay over the fast one. Measure the gap, divide by the per-kilometre difference, and the distance falls out — one hammer blow, no stopwatch at the far end needed. **11.** The [rail-sound](https://one-course.com/books/physics/1/en/chapter/19-sound-around-us#def-g3-sound-around-us-sound): fog is a crowd of droplets that scatters *[light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)* hopelessly but barely troubles a relay locked inside [solid](https://one-course.com/books/physics/1/en/chapter/14-solids-liquids-gases#def-g3-solids-liquids-gases-solid) steel ([air-sound](https://one-course.com/books/physics/1/en/chapter/19-sound-around-us#def-g3-sound-around-us-sound) too survives fog well — but the rail’s message is the cleanest and fastest of the three). **12.** For example: “Every [echo](https://one-course.com/books/physics/1/en/chapter/27-how-sound-travels#ex-g4-how-sound-travels-echo) pays for the round trip: halve before believing. Every [medium](#def-g7-sound-production-medium) sets its own pace: choose the [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) with the crowd, never by habit. And every timing in this canyon started with the eye — [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)’s trip counts as instant here, which is why seeing the hammer fall may serve as the starting gun.”