A sound wave has a frequency of 4 kHz and wavelength 30 cm. How long w

A sound wave has a frequency of 4 kHz and wavelength 30 cm. How long will it take to travel 2.4 km ?

[amp_mcq option1=”2.0 s” option2=”0.6 s” option3=”1.0 s” option4=”8.0 s” correct=”option1″]

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UPSC CDS-2 – 2021

To find the time taken, we first need to calculate the speed of the sound wave using the formula speed (v) = frequency (f) × wavelength (λ). Given f = 4 kHz = 4000 Hz and λ = 30 cm = 0.3 m, the speed is v = 4000 Hz × 0.3 m = 1200 m/s. The distance to travel is 2.4 km = 2400 m. Time (t) = distance (d) / speed (v) = 2400 m / 1200 m/s = 2 seconds.

The speed of a wave is the product of its frequency and wavelength (v = fλ). Time taken to travel a distance is distance divided by speed (t = d/v). Ensure units are consistent (e.g., meters and seconds).

Frequency is the number of waves passing a point per second (Hz), and wavelength is the distance between successive crests or troughs (m). Kilohertz (kHz) is 1000 Hz, and a kilometer (km) is 1000 meters. Centimeter (cm) is 0.01 meters. Proper unit conversion is crucial for calculations.

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