Speed, Distance and Time; Light against Sound
On a monsoon evening you see a flash of lightning – and only a few seconds later you hear the thunder. Both happen at the same moment, so why the delay? Your textbook (page 164) answers with the speed of sound (ശബ്ദവേഗം) and a simple calculation: distance = speed × time. This page teaches that formula from scratch – what speed means, the units m/s and km/h, how to rearrange the formula – and then races light against sound.
- Multiplying and dividing; multiplying and dividing by 1000.
- Powers of ten: 108 means 1 followed by 8 zeros.
1. What is speed?
Speed tells you how much distance is covered in one unit of time. If a cyclist goes 50 m every 10 s, she covers 5 m in each second: her speed is 5 metres per second, written 5 m/s.
The SI unit of speed is the metre per second (m/s). Vehicles use kilometres per hour (km/h). The speed of sound in air is about 350 m/s – your textbook's Table 8.3 gives 347 m/s at 25 °C, and uses 350 m/s in its example.
The race runs in real time for 10 seconds. Speeds used: walking 1.5 m/s, cycling 5 m/s, KSRTC bus 15 m/s, sound in air 350 m/s. Time taken = distance ÷ speed.
2. Units: m/s and km/h
To change between the two units, remember 1 km = 1000 m and 1 h = 60 × 60 = 3600 s:
Slide all the way to 1260 km/h: that is the speed of sound in air, 350 m/s – faster than a passenger jet (about 900 km/h = 250 m/s).
Worked example 1 · The KSRTC bus
Q. A KSRTC bus travels 54 km in 1 hour on a straight highway. Find its speed in m/s.
Change the distance into metres (× 1000) and the time into seconds (1 h = 3600 s) first. Then divide.
3. Rearranging the formula
The same three quantities can be arranged three ways. Cover the one you want in the triangle, and the other two show you what to do:
d on top, v and t at the bottom. Covering d leaves v × t (side by side = multiply). Covering v leaves d over t (one above the other = divide); covering t leaves d over v.
| To find | Formula | Example with sound in air (350 m/s) |
|---|---|---|
| distance | d = v × t | in 4 s sound travels 350 × 4 = 1400 m |
| speed | v = d ÷ t | 1400 m in 4 s → 1400 ÷ 4 = 350 m/s |
| time | t = d ÷ v | to cover 700 m: 700 ÷ 350 = 2 s |
4. Light against sound
Light is astonishingly fast: about 3 × 108 m/s – that is 300 000 000 m (300 000 km) every second. Sound in air covers only about 350 m in a second. So light is almost a million times faster (3 × 108 ÷ 350 ≈ 860 000). Over a few kilometres, light arrives in a few millionths of a second – practically instantly – while sound needs several seconds. That is why you see lightning, fireworks or a distant hammer blow before you hear them.
The sound front moves in real time at 350 m/s. The light covers the distance in a few microseconds (1 µs = one millionth of a second) – far too short to notice. So the gap you hear is the time the sound takes.
Watch the Thrissur Pooram fireworks (vedikkettu) from a kilometre away: the sky lights up first, and the boom arrives about 3 seconds later. In the monsoon, count the seconds between a lightning flash and its thunder: every 3 seconds means about 1 km (1000 m ÷ 350 m/s ≈ 2.9 s). At a cricket match in the Greenfield Stadium, Karyavattom, people in the far stands see the bat hit the ball a moment before they hear the “tock”.
Worked example 2 · The firecracker (textbook page 164)
Q. At night you see the light of a firecracker and hear its sound 3 seconds later. If the speed of sound is 350 m/s, how far away did the firecracker burst?
The light reached you almost instantly, so the sound took the full 3 s. Use distance = speed × time.
Worked example 3 · How far is the storm?
Q. During a thunderstorm, Meera counts 6 seconds between a lightning flash and the thunder. Taking the speed of sound as 350 m/s, find the distance of the lightning (a) in metres, (b) in kilometres.
Distance = speed × time. To change metres into kilometres, divide by 1000.
- speed = distance ÷ time; distance = speed × time; time = distance ÷ speed.
- Units: m/s (SI) and km/h; km/h ÷ 3.6 = m/s.
- Light: about 3 × 108 m/s – practically instant over everyday distances. Sound in air: about 350 m/s.
- The delay between seeing and hearing is the time the sound takes: distance = 350 × (gap in seconds).