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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= λ T .
- Since ν= 1 T , we get v=λ×ν — 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 λ= v ν with v=344 m/s : for 20 Hz, λ= 344 20 =17.2 m ; for 20 kHz, λ= 344 20000 =0.0172 m =1.72 cm .
Time delay 5 s, v=340 m/s . Distance =v× t=340× 5=1700 m ≈ 1.7 km .
From the graph, λ=50 m , speed in steel =5000 m/s . Frequency ν= v λ = 5000 50 =100 Hz ; time period T= 1 ν =0.01 s .
- What if the speed of sound in air depended on frequency?
- High and low notes would then travel at different speeds.
- Notes from a singer and instruments would arrive at different times.
- Music would reach us jumbled and unpleasant.
- In real air the speed depends only on the medium.
- So all notes arrive together and 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. Table 10.1 gives the speed of sound in three media.
- Water : air =1500:340≈ 4.4:1 .
- Steel : water =5000:1500≈ 3.3:1 .
- So sound is fastest in solids, slower in liquids, slowest in gases.
NCERT Question 9 — A source produces a sound
NCERT Question 12 — The speed of sound in
NCERT Question 15 — Two identical sound sources are
- In most media, such as air, the speed of sound depends only on the medium .
- It does not depend on the source or on the frequency.
- If the source frequency changes, the wavelength changes.
- But the speed stays constant.
- Some special materials can behave differently.
- Porous foams and engineered structures are examples.
- 11. Two friends stand along a steel fence 340 m apart. Gunjan puts her ear on the fence; her friend knocks it. Using Table 10.1, find the time difference between the sound through air and through steel. Could she tell the two sounds apart?
- Through air : t= 340 m 340 m s -1 =1 s .
- Through steel : t= 340 m 5000 m s -1 =0.068 s .
- Time difference =1-0.068= 0.932 s .
- Two sounds need a gap of at least 0.1 s to be heard separately.
- 0.932 s is far more than 0.1 s, so yes — she can distinguish them.
- Speed of sound — the distance a point on the wave travels per unit time; speed equals wavelength times frequency.
