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A bat emits the ultrasonic sound of frequency $100 kHz$ in the air. If this sound meets a water surface, what is the wavelength of the transmitted sound? Speed of sound in air $= 340 m s^{- 1}$ , and in water $= 1500 m s^{- 1}$ .

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15 mm

10 mm

12 mm

20 mm

answer is A.

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Detailed Solution

The wavelength of the transmitted sound is

15 mm .

Here,
The ultrasonic sound of frequency

v = 100 kHz

\Rightarrow

v = 100 \times 10^{3} Hz

\Rightarrow 10^{5} Hz = 10^{5} s^{- 1}

Speed of sound in air

v_{a} = 340 m s^{- 1}

Speed of sound in water

v_{w} = 1500 m s^{- 1}

The frequency of both the reflected and transmitted sound remains unchanged.
Wavelength of transmitted sound,

λ_{w} = \frac{v_{w}}{v}

= \frac{1500 m s^{- 1}}{10^{5} s^{- 1}}

= 15 \times 10^{- 3} m

= 15 mm

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