NEET Physics - Chapter 17

Velocity of Longitudinal Wave (Sound Wave) – Complete Notes, Revision, Important Questions & Downloads

Velocity of Longitudinal Wave (Sound Wave) is organized around the subtopic Sound Velocity in Different Media, where the governing relation is v = sqrt(E/rho). NEET tests this topic through direct formula checks, medium-comparison statements, and Newton versus Laplace correction numericals in air. You must identify the correct elastic modulus first: v = sqrt(Y/rho) in solids and v = sqrt(B/rho) in liquids and gases, then apply thermodynamic condition for gases. The standard benchmark trap is Newton's isothermal prediction 280 m/s versus Laplace-corrected adiabatic value 332 m/s for air.

⬇ Download Notes PDF View Important Questions →

Formula-DrivenConcept + NumericalNCERT-Aligned

Expected QuestionsQ

Typically one direct or mixed question appears on medium dependence or Newton-Laplace correction.

Time Required⏱

1.5 h

Around 50 minutes to lock formula map and 40 minutes for MCQs, plus 20 minutes for error-log revision.

Difficulty⚡

Medium

Equations are short, but students lose marks by mixing isothermal and adiabatic assumptions or wrong modulus selection.

NRI USA Curriculum GapUS

Moderate Bridge Needed

Many US school tracks treat sound speed qualitatively, while NEET expects equation-level fluency with modulus and thermodynamic-process conditions.

5Subtopics

18Practice Questions

4Free Downloads

1.5 hPrep Time

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Velocity of Longitudinal Wave (Sound Wave) Weightage and Trend

Waves and Sound - Topic 7

NEET Year	Questions from this Topic	Bar	Marks
2020	1	1 question	4
2021	0	0 question	0
2022	1	1 question	4
2023	0	0 question	0
2024	1	1 question	4
2025	0	0 question	0
Estimated topic-linked asks in recent NEET papers	3		12

The first decision in every question is modulus choice: Young's modulus for solid rods, bulk modulus for liquids and gases.
In air, Newton's isothermal assumption gives approximately 280 m/s, while Laplace's adiabatic correction gives approximately 332 m/s.
A frequent mixed item links v_sound with molecular motion using v_sound / v_rms = sqrt(gamma/3).

📊

0.5

Avg Questions / Year

🎯

Total Marks (6 yrs)

📈

Mixed

Pattern

⚠️

Medium

Difficulty

5-Step Modulus-to-Process Solving Routine

Write the master relation before substitution Start with v = sqrt(E/rho), then replace E only after identifying whether the medium is solid, liquid, or gas.

Pick modulus from the stem, not from memory bias For solids use Y, for liquids and gases use B; if the question is about crust-like extended solids, use B + (4/3)eta.

Lock gas-process assumption explicitly If the stem implies rapid compression-rarefaction in air, use adiabatic elasticity B = gamma P, not isothermal B = P.

Use Newton and Laplace as calibration numbers Remember 280 m/s from Newton's isothermal estimate and 332 m/s from Laplace correction to quickly reject wrong options.

Cross-check ratio relations at the end When molecular speed appears, verify with v_sound / v_rms = sqrt(gamma/3); if the trend contradicts this ratio, your setup is wrong.

Velocity of Longitudinal Wave (Sound Wave) Download Kit

PDF · Cheat Sheet · MCQ Set · PYQ

📘

Full Notes

Complete notes covering v = sqrt(E/rho), modulus selection across media, Newton's formula, Laplace correction, and ratio with rms speed.

10 pagesFormula + condition map

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🧾

Formula Sheet

One-page formula stack for v = sqrt(Y/rho), v = sqrt(B/rho), v = sqrt(gamma RT/M), and v_sound / v_rms = sqrt(gamma/3).

2 pagesLast-day revision

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🧠

MCQ Practice

Condition-driven MCQ set where the correct answer depends on identifying modulus type and thermodynamic process in air.

60 MCQsAnswer key included

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📂

PYQ Workbook

Chapter-level PYQ workbook focused on speed-of-sound medium comparisons and Newton-Laplace correction style options.

Year taggedTrap-first solutions

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Subtopics in Velocity of Longitudinal Wave (Sound Wave)

2-Column Table

Column A	Column B
Sound Velocity in Different Media↗	Newton's formula↗
Laplace correction↗	Effect of temperature↗
Effect of humidity↗

Rapid Revision Cards

Concept → Trap → Example

1) Sound Velocity in Different Media

Formula and condition lock

Velocity of sound in any elastic medium is v = sqrt(E/rho); in solids v = sqrt(Y/rho), and in liquids or gases v = sqrt(B/rho).

Choose modulus from medium type first, then evaluate density effect; this prevents cross-medium formula mixing.
For air, Newton used isothermal B = P and obtained about 280 m/s, but Laplace used adiabatic B = gamma P and matched about 332 m/s.
Trap: treating gas propagation as isothermal in NEET numericals gives systematically low answers and wrong option elimination.

Example (NEET-style)For air near NTP, Newton gives v = sqrt(P/rho) = 280 m/s with P = 1.01 x 10^5 N/m^2 and rho = 1.29 kg/m^3. Applying Laplace correction with gamma = 1.41 gives v = sqrt(1.41) x 280 about 332 m/s, which matches experiment.

Curriculum Gap: India vs USA

Two concrete preparation gaps to bridge for NEET readiness

AP Physics 1 wave unit vs NEET modulus-centric sound speed

AP Physics 1 usually emphasizes qualitative wave behavior and may not train rapid switching among Young's modulus, bulk modulus, and adiabatic elasticity for sound speed.

Build a one-page map: medium -> elasticity term -> velocity formula, then rehearse with timed identification drills.
Solve 15 items where only one line in the stem reveals whether Y, B, or gamma P must be used.

US classroom derivation pace vs NEET option-elimination speed

US coursework often allows longer written reasoning, but NEET requires fast numerical discrimination using benchmark values like 280 m/s and 332 m/s in under a minute.

Practice ten Newton-versus-Laplace comparisons with strict 45-second limits per question.
Memorize the ratio form v_sound / v_rms = sqrt(gamma/3) and use it for sanity checks during mixed gas-kinetic MCQs.

NEET-style practice questions

1 MCQ

1A question stem states that sound propagation in air is a rapid compression-rarefaction process and gives P and rho at NTP. If a student uses v = sqrt(P/rho) and gets 280 m/s, what is the most accurate correction pathway to obtain the physically correct speed?Sound Velocity in Different Media

Keep isothermal assumption and multiply by sqrt(3/2)

Replace P by gamma P (adiabatic elasticity) and compute v = sqrt(gamma P/rho), giving about 332 m/s

Replace rho by rho/gamma only and keep v = sqrt(P/rho), giving exactly 280 m/s

Use v = sqrt(Y/rho) because air behaves like a stretched solid

The stem explicitly indicates rapid compression-rarefaction in a gas, so the thermodynamic process is adiabatic, not isothermal. Newton's estimate v = sqrt(P/rho) assumes isothermal elasticity B = P and underestimates speed at about 280 m/s. Laplace correction states B = gamma P, hence v = sqrt(B/rho) = sqrt(gamma P/rho). For air, gamma is approximately 1.41, so v_corrected = sqrt(1.41) x 280 approximately 332 m/s, consistent with measured value. Option A uses an arbitrary factor not derived from gas thermodynamics. Option C changes density without physical basis and still preserves Newton's incorrect structure. Option D is wrong because Y applies to solids under tensile/compressive longitudinal wave treatment, not gases where bulk modulus governs pressure waves.

Practice Questions

Click "Reveal Answer" after attempting

1The speed of sound in a medium is v = sqrt(E/rho). If two solids have the same density but Young's moduli in the ratio 9:4, what is the ratio of sound speeds v1:v2?

9:4

3:2

2:3

81:16

👁 Reveal Answer

Correct option: 3:2. For solids, E = Y so v = sqrt(Y/rho). With equal density, speed ratio is sqrt(Y1/Y2) = sqrt(9/4) = 3/2. Option 9:4 is the trap from forgetting square root. Option 2:3 reverses numerator and denominator. Option 81:16 is from squaring instead of taking root.

2Newton's estimate for speed of sound in air is 280 m/s. Taking gamma = 1.41, what value follows from Laplace correction?

332 m/s

236 m/s

395 m/s

280 m/s

👁 Reveal Answer

Correct option: 332 m/s. Laplace correction uses adiabatic elasticity, so v = sqrt(gamma) x v_Newton = sqrt(1.41) x 280. Since sqrt(1.41) is about 1.187, corrected speed is approximately 1.187 x 280 about 332 m/s. Option 236 m/s would require dividing by sqrt(gamma), which is physically opposite. Option 395 m/s comes from multiplying by gamma directly without square root. Option 280 m/s ignores the correction.

3For a gas, v_sound = sqrt(gamma RT/M) and v_rms = sqrt(3RT/M). If gamma = 1.2, find v_sound/v_rms.

sqrt(3/1.2)

sqrt(1.2/3)

1.2/3

3/1.2

👁 Reveal Answer

Correct option: sqrt(1.2/3). Divide the two expressions: v_sound/v_rms = sqrt((gamma RT/M)/(3RT/M)) = sqrt(gamma/3). Substituting gamma = 1.2 gives sqrt(1.2/3). Option sqrt(3/1.2) is inverse ratio, while 1.2/3 and 3/1.2 miss the required square root.

4In a liquid medium, bulk modulus doubles and density becomes eight times. How does sound speed change?

Becomes half

Becomes one-fourth

Becomes sqrt(2)

Remains same

👁 Reveal Answer

Correct option: Becomes half. In liquids, v = sqrt(B/rho). New speed ratio is v2/v1 = sqrt((2B)/(8rho)) = sqrt(1/4) = 1/2. Option one-fourth forgets square root. Option sqrt(2) ignores density increase. Option remains same would require equal scaling of B and rho, which is not given here.

Physics Revision Checklist

Check off chapters as you revise

Use this section for quick chapter tracking before mocks, part tests, and final NEET revision.

Sound Velocity in Different Media: Build the modulus mapWrite a three-row table for solid, liquid, and gas with corresponding elasticity term and velocity formula, then solve one example from each row.

Sound Velocity in Different Media: Newton-Laplace correction drillReproduce the 280 m/s to 332 m/s correction from memory using gamma = 1.41 and explain why isothermal assumption underestimates speed.

Sound Velocity in Different Media: Unit and dimension checkAfter every numerical, verify that elasticity over density has SI unit m^2/s^2 and final velocity is reported in m/s.

Sound Velocity in Different Media: Medium-comparison practiceSolve five ordering questions using elasticity and density logic to justify why sound is fastest in solids and slowest in gases.

Sound Velocity in Different Media: Gas kinetic relation validationDerive v_sound / v_rms = sqrt(gamma/3) once, then use it to check consistency in two mixed thermodynamics-wave MCQs.

Frequently Asked Questions

Notes · Downloads · Revision · Important Questions

Why is the general speed formula written as v = sqrt(E/rho)?

For mechanical longitudinal waves, propagation speed depends on how strongly the medium resists compression or extension and how much inertia it has. Elastic response contributes the restoring factor E, and density rho contributes inertia. Their ratio sets acceleration scale, so v emerges as the square root of E/rho.

Why do we use Young's modulus in solids but bulk modulus in fluids?

In solids, longitudinal disturbances can involve elastic response associated with stretching and compression along material structure, so Young's modulus appears in the simplified rod model. In fluids, shear rigidity is negligible for this context and pressure-volume compression dominates, so bulk modulus is the correct restoring parameter.

Why did Newton's formula give a lower speed than experiment?

Newton assumed the compression and rarefaction process in air to be isothermal, giving B = P and v around 280 m/s. Real sound propagation is rapid, allowing negligible heat exchange, so the process is closer to adiabatic with B = gamma P. This larger effective elasticity increases predicted speed to the observed range near 332 m/s.

Is Laplace correction only a numerical patch or a physical model change?

It is a physical-model correction, not an arbitrary numerical adjustment. The key change is thermodynamic assumption: isothermal to adiabatic. Once that is changed, elasticity increases from P to gamma P, and the corrected speed follows naturally from the same velocity framework without adding empirical fudge factors.

Why is sound typically faster in solids than in gases?

Although solids can be denser, their elastic moduli are usually much larger than those of gases, and the ratio E/rho is generally higher. Since velocity depends on square root of this ratio, the high elasticity effect dominates. That is why typical values are around 5000 m/s in solids, 1500 m/s in water, and around 330 m/s in air.

When should I use v = sqrt(gamma RT/M) instead of v = sqrt(gamma P/rho)?

Both are equivalent for ideal gases. Use v = sqrt(gamma RT/M) when temperature and molar mass are directly given, or when comparing gases by composition and temperature. Use v = sqrt(gamma P/rho) when pressure-density form is explicit in the statement. Switching forms based on given data saves time and avoids algebraic mistakes.

How is the relation with rms molecular speed useful in NEET?

The relation v_sound / v_rms = sqrt(gamma/3) provides a fast check for ratio questions combining kinetic theory and sound propagation. If an option implies v_sound equals or exceeds v_rms for common gamma values, it is usually wrong. This relation helps eliminate distractors quickly without full recalculation.

What is the quickest error-check sequence for this topic in exam conditions?

Use a fixed four-step check: identify medium, choose modulus, choose thermodynamic process for gases, then test numerical reasonableness against known benchmarks such as 280 m/s versus 332 m/s in air. If your final value conflicts with these baseline expectations, recheck the assumption before marking the answer.

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Velocity of Longitudinal Wave (Sound Wave)

Velocity of Longitudinal Wave (Sound Wave) – Complete Notes, Revision, Important Questions & Downloads

1) Sound Velocity in Different Media

AP Physics 1 wave unit vs NEET modulus-centric sound speed

US classroom derivation pace vs NEET option-elimination speed

Physics Revision Checklist

NEET NRI Counseling & Admission eBook Download

Schedule Trial Session For NEET Prep

Sound Velocity in Different Media

Newton's formula

Laplace correction

Effect of temperature

Effect of humidity

Subtopics

Sound Velocity in Different Media

Newton's formula

Laplace correction

Effect of temperature

Effect of humidity

NEET > Physics > Oscillations and Waves Chapters

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Velocity of Longitudinal Wave (Sound Wave)

Overview content

Velocity of Longitudinal Wave (Sound Wave) – Complete Notes, Revision, Important Questions & Downloads

1) Sound Velocity in Different Media

AP Physics 1 wave unit vs NEET modulus-centric sound speed

US classroom derivation pace vs NEET option-elimination speed

Physics Revision Checklist

NEET NRI Counseling & Admission eBook Download

Schedule Trial Session For NEET Prep

Sound Velocity in Different Media

Newton's formula

Laplace correction

Effect of temperature

Effect of humidity

Subtopics

Sound Velocity in Different Media

Newton's formula

Laplace correction

Effect of temperature

Effect of humidity

NEET > Physics > Oscillations and Waves Chapters

Comments

Leave a comment

Comments (0)