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
Correct answer
Explanation
The correct answer is C, 3.0 s. The speed of the wave is frequency times wavelength, 700 m/s, and 2,100 m at 700 m/s takes 3 seconds.
For any wave, speed v = f × λ. Here f = 2 kHz = 2,000 Hz and λ = 35 cm = 0.35 m, so v = 2,000 × 0.35 = 700 m/s. The distance is 2.1 km = 2,100 m, and time = distance ÷ speed = 2,100 ÷ 700 = 3 s. The two traps are units: kilohertz must become hertz, centimetres must become metres and kilometres must become metres before you divide. The frequency of a sound is fixed by its source, while its speed and wavelength depend on the medium.
A is wrong: 30 s comes from a slip of one power of ten in the unit conversion.
B is wrong: 2.1 s simply repeats the distance figure and is not the result of any correct working.
D is wrong: 4.1 s does not follow from v = fλ with these values.
Exam tip: v = fλ, then t = d/v — convert kHz to Hz, cm to m and km to m first.
Practice Questions
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