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A bat emits ultrasonic sound of frequency $1000 \mathrm{kHz}$ in air. If the sound meets a water surface, what is the wavelength of (a) the reflected sound, (b) the transmitted sound? [Speed of sound in air $=340 \mathrm{~m} / \mathrm{s}$ and in water $=1486 \mathrm{~m} / \mathrm{s}]$
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Verified Answer
According to question,
$$
v=1000 \mathrm{kHz}=10^6 \mathrm{~Hz}, v_a=340 \mathrm{~m} / \mathrm{s} \text {, }
$$
$v_{\mathrm{w}}=1486 \mathrm{~m} / \mathrm{s}$
(a) Wavelength of reflected sound
$$
=\lambda_a=\frac{v_a}{v}=\frac{340}{10^6}=3.4 \times 10^{-4} \mathrm{~m}
$$
(b) Wavelength of transmitted sound
$$
=\lambda_{\mathrm{w}}=\frac{v_{\mathrm{w}}}{\mathrm{v}}=\frac{1486}{10^6}=1.486 \times 10^{-3} \mathrm{~m}
$$
$$
v=1000 \mathrm{kHz}=10^6 \mathrm{~Hz}, v_a=340 \mathrm{~m} / \mathrm{s} \text {, }
$$
$v_{\mathrm{w}}=1486 \mathrm{~m} / \mathrm{s}$
(a) Wavelength of reflected sound
$$
=\lambda_a=\frac{v_a}{v}=\frac{340}{10^6}=3.4 \times 10^{-4} \mathrm{~m}
$$
(b) Wavelength of transmitted sound
$$
=\lambda_{\mathrm{w}}=\frac{v_{\mathrm{w}}}{\mathrm{v}}=\frac{1486}{10^6}=1.486 \times 10^{-3} \mathrm{~m}
$$
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