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CGP EDU Academic Team
Published on: September 12, 2026
A plane wave of sound travelling in air is incident upon a plane water surface. The angle of incidence is 60º. Assuming. snell’s law to be valid for sound waves, it follows that the sound wave will be refracted into water away from the normal.
Text Solution
Verified by ExpertsThe correct answer is:
B
To solve this problem, we will use Snell's law, which states that \( n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \).
Now, substitute the values into Snell's law:
\( 1.00 \cdot \sin(60^\circ) = 1.33 \cdot \sin(\theta_2) \).
The sine of 60 degrees is approximately 0.866. Therefore:
\( 0.866 = 1.33 \cdot \sin(\theta_2) \).
Solving for \( \sin(\theta_2) \):
\( \sin(\theta_2) = \frac{0.866}{1.33} \approx 0.651 \).
Thus, \( \theta_2 = \sin^{-1}(0.651) \approx 40.5^\circ \).
Since 40.5º is less than 60º, the sound wave is indeed refracted towards the normal (not away from it). Therefore, the statement in the question is incorrect.
- Let \( n_1 \) be the refractive index of air (approximately 1.00).
- Let \( n_2 \) be the refractive index of water (approximately 1.33).
- The angle of incidence \( \theta_1 = 60^\circ \).
Now, substitute the values into Snell's law:
\( 1.00 \cdot \sin(60^\circ) = 1.33 \cdot \sin(\theta_2) \).
The sine of 60 degrees is approximately 0.866. Therefore:
\( 0.866 = 1.33 \cdot \sin(\theta_2) \).
Solving for \( \sin(\theta_2) \):
\( \sin(\theta_2) = \frac{0.866}{1.33} \approx 0.651 \).
Thus, \( \theta_2 = \sin^{-1}(0.651) \approx 40.5^\circ \).
Since 40.5º is less than 60º, the sound wave is indeed refracted towards the normal (not away from it). Therefore, the statement in the question is incorrect.
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