CAPF AC 2023 Q34: Science & Technology – Physics
A sound wave of frequency of 2 kHz has a wavelength of 35 cm in a given medium. How long will it take to travel a distance of 2.1 km through the medium?
- (a) 30 s
- (b) 2.1 s
- (c) 3.0 s
- (d) 4.1 s
Answer: (c) 3.0 s
Explanation
Time taken by a sound wave
Given: frequency f = 2 kHz = 2000 Hz, wavelength λ = 35 cm = 0.35 m, distance d = 2.1 km = 2100 m.
How to think: first find the speed of the wave from f and λ, then divide the distance by that speed.
| Step | Working | Result |
|---|---|---|
| Speed of the wave | v = f × λ = 2000 × 0.35 | 700 m/s |
| Time for 2100 m | t = d ÷ v = 2100 ÷ 700 | 3 s |
Check: 700 m/s × 3 s = 2100 m, which is the distance given.
Answer: (c) 3.0 s.
Why each option is right or wrong
- (a) Incorrect. 30 s comes from a slip of a factor of ten in the speed or the distance.
- (b) Incorrect. 2.1 s is the distance in km written as seconds, with no division by the speed.
- (c) CORRECT. Speed is 2000 × 0.35 = 700 m/s, so time is 2100 ÷ 700 = 3.0 s.
- (d) Incorrect. 4.1 s does not follow from v = fλ and t = d ÷ v.
Key point
Wave speed: v = f × λ. Time = distance ÷ speed. Convert units first: 1 kHz = 1000 Hz, 1 cm = 0.01 m, 1 km = 1000 m. Sound in air is about 340 m/s; here the medium gives 700 m/s.
Remember
v = fλ first, then time = distance ÷ v.
Common mistakes
- Forgetting to convert cm to m and km to m before dividing.
- Using 340 m/s (speed of sound in air) instead of the speed found from f × λ.
- Multiplying the distance by the speed instead of dividing.
Exam tip
Educated guess: 2 × 35 = 70 gives 700 m/s after the unit conversion, and 2100 divided by 700 is a clean 3. A clean answer in the options, (c), is the sign you have the right track.
Sources
- NCERT Class IX Science — Sound, Chapter 12 (speed, wavelength and frequency: v = νλ)
- NCERT Class XI Physics Part II — Waves, Chapter 14