Question 15
Two identical sound sources are placed at A and B — one in air and one submerged in water (Fig. 10.34). Both produce sounds at the same time, which travel horizontally to the vertical side of the cliff and come back. If the time taken by the sound to return to A is 4.5 times than that of B, what is the ratio between the speeds of sound in air and water?
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  • Same distance, so time is inversely proportional to speed: \(\dfrac{t_A}{t_B}=\dfrac{v_B}{v_A}=4.5\).
  • Hence \(\dfrac{v_{\text{air}}}{v_{\text{water}}}=\dfrac{v_A}{v_B}=\dfrac{1}{4.5}\approx \mathbf{1:4.5}\) (sound is faster in water).
Ratio of Speeds Same distance, so time is inverse of speed t_A / t_B = v_B / v_A = 4.5 v_air to v_water is about 1 to 4.5
Back to: 10.6.3 Speed of Sound
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