A sound wave has a frequency of 1 kHz and wavelength 50 cm. How long will it take to travel 1 km?
- (a)5 s
- (b)4 s
- (c)3 s
- (d)2 s
Correct — D, 2 s. First find the wave speed: v = f × λ = 1000 Hz × 0.50 m = 500 m/s (1 kHz = 1000 Hz and 50 cm = 0.50 m). Then time = distance ÷ speed = 1000 m ÷ 500 m/s = 2 s.
- (a)5 s — This would require a speed of only 200 m/s, but v = f × λ gives 500 m/s here.
- (b)4 s — This corresponds to a speed of 250 m/s, which is not what f × λ gives (500 m/s).
- (c)3 s — This implies a speed of about 333 m/s (close to sound in air), but the question's own f and λ fix the speed at 500 m/s.
For any wave, speed = frequency × wavelength (v = f·λ). Once the speed is known, the time to cover a distance follows from time = distance ÷ speed. The wave's own frequency and wavelength set its speed here, so you do not use the textbook 340 m/s for air.
The two easy slips are unit conversion (1 kHz = 1000 Hz, 50 cm = 0.5 m) and grabbing the familiar 'speed of sound in air' instead of computing v from the given f and λ.
- Wave relation: v = f × λ.
- 1 kHz = 1000 Hz; 50 cm = 0.50 m.
- v = 1000 × 0.50 = 500 m/s for this wave.
- Time = distance ÷ speed = 1000 ÷ 500 = 2 s.
Compute the wave speed from f × λ, then divide the distance by that speed.
- Forgetting to convert 50 cm to 0.5 m or 1 kHz to 1000 Hz.
- Using 340 m/s (sound in air) instead of the speed given by this wave's own f and λ.
Compute the wave speed from f and λ, then use time = distance ÷ speed.
No directly related past PYQ was found.
- practice — not a real PYQ
A wave of frequency 500 Hz and wavelength 2 m has a speed of
- (a)250 m/s
- (b)1000 m/s
- (c)502 m/s
- (d)0.004 m/s
Answer(b) 1000 m/s — v = f × λ = 500 × 2.
- practice — not a real PYQ
If the speed of a sound wave is 340 m/s and its frequency is 170 Hz, its wavelength is
- (a)0.5 m
- (b)1 m
- (c)2 m
- (d)5 m
Answer(c) 2 m — λ = v ÷ f = 340 ÷ 170.