A sound wave of frequency of 2 kHz has a wavelength of 35 cm in a give

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 ?

30 s
2⋅1 s
3⋅0 s
4⋅1 s
This question was previously asked in
UPSC CAPF – 2023
The correct answer is C. We need to calculate the time taken using the relationship between speed, distance, and time, after first determining the speed of the sound wave.
– The speed of a wave ($v$) is given by the product of its frequency ($f$) and wavelength ($\lambda$): $v = f \times \lambda$.
– Given $f = 2 \text{ kHz} = 2000 \text{ Hz}$ and $\lambda = 35 \text{ cm} = 0.35 \text{ m}$.
– Speed $v = 2000 \text{ Hz} \times 0.35 \text{ m} = 700 \text{ m/s}$.
– The time ($t$) taken to travel a distance ($d$) is given by $t = d / v$.
– Given $d = 2.1 \text{ km} = 2100 \text{ m}$.
– Time $t = 2100 \text{ m} / 700 \text{ m/s} = 3 \text{ seconds}$.
The units were carefully converted to meters and seconds before calculation to ensure consistency in the final answer. The frequency is given in kilohertz (kHz) and the wavelength in centimeters (cm), requiring conversion to standard SI units (Hz and m). The distance is given in kilometers (km), also requiring conversion to meters.
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