A student stands 170 m from a vertical cliff face on a calm day with no wind. She claps her hands once sharply and hears the echo from the cliff after a mea...

Marking Scheme

• (a) [1] Total distance = 2 x 170 = 340 m
• (b) [1+1] speed = distance/time = 340/1.0 = 340 m/s
• (c) [1] Some sound energy is absorbed by the cliff and the sound spreads out over a larger area, so less energy reaches the student on return
• (d) [1+1] The round trip to the second cliff is 2 x 500 = 1000 m, giving an echo time of about 2.9 s; the sound has travelled much further so it is much quieter and may be too faint to hear

Explanation

(a) The sound must travel from the student to the cliff and back again. The total distance is therefore twice the distance to the cliff: \(2 \times 170 = 340\) m. This is the key principle behind echo-based distance measurement.

(b) Using \(\text{speed} = \frac{\text{distance}}{\text{time}}\): \(v = \frac{340}{1.0} = 340\) m/s. This is consistent with the accepted value for the speed of sound in air at around 18-20 degrees C. The echo method is a practical way to measure the speed of sound outdoors.

(c) The echo is quieter than the original clap for two reasons. First, sound waves spread out spherically from the source, so the intensity (energy per unit area) decreases with distance according to the inverse square law. The sound must travel 340 m total, and the returning wavefront has spread over a much larger area than the outgoing one at the point of clapping. Second, the cliff face absorbs some of the sound energy rather than reflecting all of it - some energy is converted to heat in the rock. Together these effects mean the returning echo carries significantly less energy per unit area than the original clap.

(d) The second cliff is 500 m behind the student, so the round trip is \(2 \times 500 = 1000\) m. At 340 m/s, the echo return time would be \(\frac{1000}{340} \approx 2.94\) s. Two factors prevent a clear second echo: (1) the much greater distance means the sound has spread over a far larger area and lost much more energy, making the echo very faint; (2) the long delay (nearly 3 seconds) means the echo arrives well after the first echo and any residual reverberation, and background noise may mask it. Additionally, the cliff behind the student requires the sound to travel away from the first cliff, meaning neither cliff reinforces the other.