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

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