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What is the maximum audible wavelength at room temperature when the speed of sound is $340 m / s$ ?

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0.2 Å^{}

5 Å

17 cm

17 mm

answer is D.

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Detailed Solution

17 mm

is the maximum audible wavelength at room temperature when the speed of sound is

340 m / s

.
A human ear can hear the sound between frequencies

20 Hz

and

20000 Hz

. The frequency of a sound wave is inversely proportional to its wavelength. Hence to get the minimum wavelength of the sound wave, we have to take the maximum frequency limit of

20000 Hz

.
We know that

v = nλ

Here,

v

is the velocity of the sound wave

n

is the frequency of the sound wave

λ

is the wavelength of the sound wave

λ_{\min} = \frac{v}{n_{\max}}

= \frac{340 m / s}{20000 Hz}

λ_{\min} = 0.017 m

= 17 \times 10^{- 3} m

= 17 \times 10^{- 3} \times 10^{+ 3} mm

λ_{\min} = 17 mm

Hence the minimum audible wavelength is

17 mm

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