A sound wave having frequency of 300 Hz is travelling in an unknown medium. Its wavelength is not known. It travels a distance equal to 150 times its wavelength in time t. The value of t is :
- (a)0.5 s
- (b)1 s
- (c)1.5 s
- (d)2 s
Correct — A, 0.5 s. Distance is 150 wavelengths and speed is frequency times wavelength, so t = 150λ / (300λ) = 0.5 s — the unknown wavelength cancels, which is the whole point of the question.
- (b)1 s — 1 s would need the wave to cover 300 wavelengths, i.e. a distance equal to one second's travel at 300 Hz.
- (c)1.5 s — 1.5 s corresponds to 450 wavelengths.
- (d)2 s — 2 s corresponds to 600 wavelengths, four times the distance actually given.
For any wave, v = fλ. A frequency of 300 Hz means 300 complete wavelengths pass a point every second, so covering 150 wavelengths takes exactly half a second regardless of the medium.
The examiner deliberately withholds the wavelength and the medium to see whether you reach for a number you do not have. Because both the distance and the speed are expressed in terms of λ, it cancels — a useful habit to look for before hunting for missing data.
- v = fλ for all waves.
- 300 Hz means 300 wavelengths pass a fixed point per second.
- Time = distance / speed = 150λ / 300λ = 0.5 s.
- The answer is independent of the medium, so 'unknown medium' is not a gap in the question.
Whenever an unknown appears in both numerator and denominator, look for it to cancel.
- Assuming the problem is unsolvable because the medium is unspecified.
- Confusing frequency with speed.
Numerical wave items at this level are usually solvable by cancellation; the missing datum is deliberate.
No directly related past PYQ was found.
- practice — not a real PYQ
A wave of frequency 500 Hz travels a distance equal to 250 of its wavelengths. The time taken is
- (a)0.5 s
- (b)1 s
- (c)1.5 s
- (d)2 s
Answer(a) 0.5 s — 250λ / (500λ) = 0.5 s, the same cancellation.