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The musical notes produced by an instrument are of frequencies $256 Hz and 384 Hz$ respectively. Compare their wavelengths. Given that the speed of sound in air is $344 m / s .$

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3 : 2

2 : 3

3 : 3

2 : 2

answer is B.

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Detailed Solution

The ratio of the wavelength is

2 : 3

.
Given,
Frequency of the musical notes is

256 Hz and 384 Hz

.
the speed of sound in air is

344 m / s .

Using the formula,

v = λ \times f

Substitute the given values in the formula,

v = λ \times f

\Rightarrow 344 = λ \times 256

\Rightarrow λ_{1} = 32 / 43 m

Again

v = λ \times f

\Rightarrow 344 = λ \times 384

{\Rightarrow λ}_{2} = 48 / 43 m

Comparing the wavelengths,

λ_{1} / λ_{2} = (32 / 43) / (48 / 43)

= 2 / 3

= 2 : 3

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