Examkin

Soru

Zorluk: ZorSound Waves, Echoes, Pitch, Loudness, and Quality

An observer standing at a position between two tall parallel vertical cliffs fires a signal pistol. The observer hears the first echo reflected from the nearer cliff after 1.2 s1.2\text{ s} and the second echo reflected from the farther cliff after 1.8 s1.8\text{ s}. If the speed of sound in air is 340 m s−1340\text{ m s}^{-1}, what is the total distance between the two cliffs?

  1. A
    102 m102\text{ m}
  2. 510 m510\text{ m}Cevap
  3. C
    816 m816\text{ m}
  4. D
    1020 m1020\text{ m}

Cevap

The total distance between the two cliffs is 510 m510\text{ m}.
Because an echo involves two-way travel of sound, the distance dd from an observer to a reflecting barrier is given by d=vt2d = \frac{v t}{2}. For the nearer cliff, the distance is d1=340×1.22=204 md_1 = \frac{340 \times 1.2}{2} = 204\text{ m}. For the farther cliff, the distance is d2=340×1.82=306 md_2 = \frac{340 \times 1.8}{2} = 306\text{ m}. The total distance between the parallel cliffs is d1+d2=204 m+306 m=510 md_1 + d_2 = 204\text{ m} + 306\text{ m} = 510\text{ m}.

Adım Adım Çözüm

1
Calculate the distance from the observer to the nearer cliff
d1=v×t12=340 m s−1×1.2 s2=204 md_1 = \frac{v \times t_1}{2} = \frac{340\text{ m s}^{-1} \times 1.2\text{ s}}{2} = 204\text{ m}
An echo involves sound traveling from the observer to the cliff and back, so the one-way distance is half the total path length.
2
Calculate the distance from the observer to the farther cliff
d2=v×t22=340 m s−1×1.8 s2=306 md_2 = \frac{v \times t_2}{2} = \frac{340\text{ m s}^{-1} \times 1.8\text{ s}}{2} = 306\text{ m}
Similarly, the sound travels to the farther cliff and back in 1.8 s1.8\text{ s}.
3
Sum the two one-way distances to find the total distance between the two cliffs
D=d1+d2=204 m+306 m=510 mD = d_1 + d_2 = 204\text{ m} + 306\text{ m} = 510\text{ m}
Since the observer is positioned between the two parallel cliffs, the total separation distance is the sum of the individual distances to each cliff.

Anahtar Kavram

Echo distance calculation involving two-way sound propagation
Bu soruyu puanla

Konular

Sound Waves, Echoes, Pitch, Loudness, and Quality

Bu konudan daha fazla soru