Which of the following graphs is correct?

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) $1$. For the velocity of sound in air, $v = \sqrt{\frac{\gamma P}{\rho}}$. Since $\rho = \frac{PM}{RT}$, we have $v = \sqrt{\frac{\gamma RT}{M}}$.

Vedclass · Accepted Answer

Vedclass · Answer

(C) $1$. For the velocity of sound in air, $v = \sqrt{\frac{\gamma P}{ho}}$. Since $ho = \frac{PM}{RT}$, we have $v = \sqrt{\frac{\gamma RT}{M}}$. At constant temperature $(T)$, $v$ is independent of pressure $(P)$. Thus, the graph in option $A$ is incorrect as it shows $v$ increasing with $P$.$2$. The velocity of sound in air is $v = \sqrt{\frac{\gamma R(T_c + 273)}{M}}$. Thus, $v^2 = \frac{\gamma R}{M}(T_c + 273)$. This is a linear equation of the form $y = mx + c$ where $y = v^2$ and $x = T_c$. The graph in option $B$ shows a line passing through the origin, which is incorrect because at $T_c = 0^\circ C$, $v^2 
eq 0$.$3$. The velocity of a transverse wave in a string is $v = \sqrt{\frac{T}{\mu}}$, where $T$ is tension and $\mu$ is linear mass density. This implies $v^2 = \frac{1}{\mu}T$, or $v = \frac{1}{\sqrt{\mu}}\sqrt{T}$. This represents a parabolic relationship between $v$ and $T$. The graph in option $C$ correctly shows this parabolic dependence.Therefore, none of the individual graphs are correct as presented in the options, but based on standard physics problems of this type, option $C$ is the only physically accurate relationship depicted.

Similar Questions

Write the equation for the speed of a transverse wave on a stretched string.

$A$ perfectly elastic uniform string is suspended vertically with its upper end fixed to the ceiling and the lower end loaded with a weight. If a transverse wave is imparted to the lower end of the string,the pulse will

$A$ transverse wave propagating on a stretched string of linear density $3 \times 10^{-4} \ kg \ m^{-1}$ is represented by the equation $y = 0.2 \sin (1.5 x + 60 t)$, where $x$ is in metres and $t$ is in seconds. The tension in the string (in newton) is

The extension in a string obeying Hooke's law is $x$. The speed of sound in the stretched string is $v$. If the extension in the string is increased to $1.5x$,the speed of sound will be (in $,v$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module