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A crest covers one wavelength in one time period — that simple idea gives the whole speed formula.
- The distance a point on the wave (a crest or trough) travels in unit time.
- A crest travels one wavelength in one time period , so speed \(v=\dfrac{\lambda}{T}\).
- Since \(\nu=\dfrac{1}{T}\), we get \(v=\lambda\times\nu\) — speed = wavelength × frequency.
- Sound is fastest in solids, slower in liquids, slowest in gases .
- In air, speed increases with temperature and humidity .
- In dry air it is about 331 m/s at 0 °C and 344 m/s at 22 °C .
Using \(\lambda=\dfrac{v}{\nu}\) with \(v=344\ \text{m/s}\): for 20 Hz, \(\lambda=\dfrac{344}{20}=17.2\ \text{m}\); for 20 kHz, \(\lambda=\dfrac{344}{20000}=0.0172\ \text{m}=1.72\ \text{cm}\).
Time delay 5 s, \(v=340\ \text{m/s}\). Distance \(=v\times t=340\times 5=1700\ \text{m}\approx 1.7\ \text{km}\).
From the graph, \(\lambda=50\ \text{m}\), speed in steel \(=5000\ \text{m/s}\). Frequency \(\nu=\dfrac{v}{\lambda}=\dfrac{5000}{50}=100\ \text{Hz}\); time period \(T=\dfrac{1}{\nu}=0.01\ \text{s}\).
What if the speed of sound in air depended on its frequency? Then different notes from a singer and instruments would arrive at slightly different times and music would sound jumbled. In ordinary air the speed depends only on the medium, so music stays pleasant.
| State | Substance/Medium | Approximate speed |
|---|---|---|
| Solid | Steel | 5000 m s⁻¹ |
| Liquid | Water | 1500 m s⁻¹ |
| Gas | Air | 340 m s⁻¹ |
10. From Table 10.1, ratio of speeds: water : air \(=1500:340\approx 4.4:1\); steel : water \(=5000:1500\approx 3.3:1\). 11. Along a 340 m steel fence, air time \(=\dfrac{340}{340}=1\ \text{s}\), steel time \(=\dfrac{340}{5000}=0.068\ \text{s}\); difference \(\approx 0.93\ \text{s}>0.1\ \text{s}\), so the two sounds can be distinguished.
NCERT Question 9 — A source produces a sound
NCERT Question 12 — The speed of sound in
NCERT Question 15 — Two identical sound sources are
- Speed of sound — the distance a point on the wave travels per unit time; speed equals wavelength times frequency.
