A microphone next to a loudspeaker is 51 m from a large wall. It records a short pulse and its echo 0.3 s later. Ignore electronic delays. (a) Calculate the speed of sound. (b) Predict the delay if the distance is doubled. (c) Give two experimental precautions and explain why the recorded pulse must be short.

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340 m/s; doubled-distance delay 0.6 s; use a short pulse, measure perpendicular distance and avoid competing echoes. The measured delay covers the outward journey from loudspeaker to wall and the return journey to the microphone. Because the devices are adjacent, the total path is twice their distance from the wall. The path length is 2 × 51 = 102 m. Hence speed = distance/time = 102/0.3 = 340 m/s, assuming the sound travels through uniform air. Doubling the wall distance doubles the total path without changing the sound speed. The new delay is therefore 2 × 0.3 = 0.6 s, not four times the original value. Measure distance perpendicular to the reflecting wall, keep microphone and source close together, and avoid other reflecting objects. A short pulse gives separate start and echo signals; a long pulse could overlap its echo and make the delay ambiguous. Repeat the measurement to check consistency.

Measuring sound with an echo 6

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