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Q8 (CDS-II/2006) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Waves and acoustics Answer Verified

Which of the following represents the correct graphical variation of velocity of sound and absolute temperature?

Result
Your answer: —  ·  Correct: C
Explanation

The speed of sound (v) in an ideal gas is directly proportional to the square root of its absolute temperature (T), expressed by the formula v = √(̳RT/M) [t1][t6]. In this relationship, ̳ (ratio of specific heats), R (gas constant), and M (molar mass) are constants for a specific gas like air [t6][t8]. Mathematically, the relation v ∝ ∙T represents a parabolic curve when plotted on a v-T graph, where the velocity increases as the square root of the temperature [t2][t3]. Graph III typically represents this square root (sub-linear) growth starting from the absolute zero origin (0 K), where molecular motion and thus sound transmission theoretically cease [t7]. While speed increases with temperature, the rate of increase gradually diminishes, distinguishing it from a linear (v ∝ T) or exponential relationship [t9].

Sources

  1. [1] https://www.grc.nasa.gov/www/k-12/VirtualAero/BottleRocket/airplane/sound.html
  2. [2] https://www.sciencedirect.com/topics/engineering/sonic-velocity
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