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Chapter 10: Problem 1428

If the velocity of sound wave in humid air is \(\mathrm{v}_{\mathrm{m}}\) and that in dry air is \(\mathrm{v}_{\mathrm{d}}\), then \(\ldots \ldots\) (A) \(\mathrm{v}_{\mathrm{m}}>\mathrm{v}_{\mathrm{d}}\) (B) \(\mathrm{v}_{\mathrm{m}}<\mathrm{v}_{\mathrm{d}}\) (C) \(\mathrm{v}_{\mathrm{m}}=\mathrm{v}_{\mathrm{d}}\) \((\mathrm{D}) \mathrm{v}_{\mathrm{m}} \gg \mathrm{v}_{\mathrm{d}}\)

Short Answer

Expert verified
The short answer based on the step-by-step solution is: The velocity of sound wave in humid air, \(v_m\), is greater than that in dry air, \(v_d\) (A) \(v_m > v_d\).

Step by step solution

01

Understand the speed of sound in air formula

The speed of sound in air depends on temperature, pressure, and humidity. One formula that takes these factors into account is: \[ v = \sqrt{\frac{\gamma R T}{M}} \] Where: - \(v\) is the speed of sound - \(\gamma\) is the adiabatic index (usually 1.4 for air) - \(R\) is the specific gas constant (287 J/(kg·K) for air) - \(T\) is the absolute temperature in Kelvin - \(M\) is the molar mass of the gas in kg/mol
02

Compare vm and vd using the formula

Since both vm and vd are velocities of sound in air, they will have the same values for \(\gamma\) and \(R\). The only difference between them is the molar mass, which will be affected by the humidity. Humid air has a lower molar mass than dry air because water vapor (molar mass = 18 g/mol) is lighter than the gases that make up dry air (mostly nitrogen and oxygen, with molar masses of 28 g/mol and 32 g/mol, respectively). We can rewrite the formula for vm and vd as follows: \[ v_m = \sqrt{\frac{\gamma R T}{M_m}} \] \[ v_d = \sqrt{\frac{\gamma R T}{M_d}} \]
03

Determine the relationship between vm and vd

Since humid air has a lower molar mass (Mm) than dry air (Md), the denominator in the formula for vm will be smaller than the denominator for vd. When you divide by a smaller number, the result is larger. Therefore: \[ v_m > v_d \] So the correct answer is: (A) \(v_m > v_d\)

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Most popular questions from this chapter

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option. (a) Statement \(-1\) is true, statement \(-2\) is true; statement \(-2\) is the correct explanation of statement \(-1\). (b) Statement \(-1\) is true, statement \(-2\) is true but statement \(-2\) is not the correct explanation of statement \(-1\). (c) Statement \(-1\) is true, statement \(-2\) is false (d) Statement \(-1\) is false, statement \(-2\) is true (A) a (B) \(\mathrm{b}\) (C) \(c\) (D) \(\mathrm{d}\) Statement \(-1:\) For a particle executing SHM, the amplitude and phase is decided by its initial position and initial velocity. Statement \(-2:\) In a SHM, the amplitude and phase is dependent on the restoring force. (A) a (B) \(b\) (C) \(\mathrm{c}\) (D) \(\mathrm{d}\)

A system is executing S.H.M. with a periodic time of \(4 / 5 \mathrm{~s}\) under the influence of force \(\mathrm{F}_{1}\) When a force \(\mathrm{F}_{2}\) is applied, the periodic time is \((2 / 5) \mathrm{s}\). Now if \(\mathrm{F}_{1}\) and \(\mathrm{F}_{2}\) are applied simultaneously along the same direction, the periodic time will be......... (A) \(\\{4 /(5 \sqrt{5})\\}\) (B) \(\\{4 /(4 \sqrt{5})\\}\) (C) \(\\{8 /(4 \sqrt{5})\\}\) (D) \(\\{8 /(5 \sqrt{5})\\}\)

As shown in figure, a block A having mass \(M\) is attached to one end of a massless spring. The block is on a frictionless horizontal surface and the free end of the spring is attached to a wall. Another block B having mass ' \(\mathrm{m}\) ' is placed on top of block A. Now on displacing this system horizontally and released, it executes S.H.M. What should be the maximum amplitude of oscillation so that B does not slide off A? Coefficient of static friction between the surfaces of the block's is \(\mu\). (A) \(A_{\max }=\\{(\mu \mathrm{mg}) / \mathrm{k}\\}\) (B) \(A_{\max }=[\\{\mu(m+M) g\\} / k]\) (C) \(A_{\max }=[\\{\mu(M-\mathrm{m}) g\\} / \mathrm{k}]\) (D) \(A_{\max }=[\\{2 \mu(M+m)\\} / k]\)

If the equation for a particle performing S.H.M. is given by $\mathrm{y}=\sin 2 \mathrm{t}+\sqrt{3} \cos 2 \mathrm{t}\(, its periodic time will be \)\ldots \ldots .$ s. (A) 21 (B) \(\pi\) (C) \(2 \pi\) (D) \(4 \pi\).

What should be the speed of a source of sound moving towards a stationary listener, so that the frequency of sound heard by the listener is double the frequency of sound produced by the source? \\{Speed of sound wave is \(\mathrm{v}\\}\) (A) \(\mathrm{v}\) (B) \(2 \mathrm{v}\) (C) \(\mathrm{v} / 2\) (D) \(\mathrm{v} / 4\)
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