For a fixed distance between a source and a listener

PHYSICS · Subjective · CBSE · Physics · Sound · Sound

Problem

For a fixed distance DD between a source and a listener, let the speeds of sound in two different media be v1v_1 and v2v_2. (a) Derive an expression showing that the ratio of the times taken for the sound to cover the distance in the two media is t1t2=v2v1\dfrac{t_1}{t_2}=\dfrac{v_2}{v_1}. (b) Using D=1 kmD=1\,\text{km}, calculate the time taken for sound to travel the distance through (i) air (v=340 m/sv=340\,\text{m/s}), (ii) water (v=1500 m/sv=1500\,\text{m/s}) and (iii) steel (v=5000 m/sv=5000\,\text{m/s}). (c) By how much time does sound travelling through steel reach the listener earlier than sound travelling through air for the same distance? Comment on the practical significance of this difference.

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