Physics · Wave motion, longitudinal and transverse waves, speed of the travelling wave, displacement relation for a progressive wave
A plane sound wave passes from medium 1 into medium The speed of sound in medium
A plane sound wave passes from medium 1 into medium \( 2 . \) The speed of sound in medium 1 is \( 200 \mathrm{m} / \mathrm{s} \) and in medium 2 is \( 100 \mathrm{m} / \mathrm{s} \). The ratio of amplitude of the transmitted wave to that of incident wave is
- A. \( \frac{3}{4} \)
- B. \( \frac{4}{5} \)
- C. \( \frac{5}{6} \)
- D. \( \frac{2}{3} \)
Step-by-step solution
Assuming the two media have the same density, the characteristic impedance is proportional to the speed of sound. For normal incidence, the pressure amplitude transmission coefficient is \( t_p = \frac{2Z_2}{Z_1+Z_2} = \frac{2c_2}{c_1+c_2} = \frac{2\times100}{200+100} = \frac{2}{3} \). Thus the ratio of transmitted to incident amplitude is \( \frac{2}{3} \).
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