NEET Physics - Chapter 17
Velocity of Transverse Wave – Complete Notes, Revision, Important Questions & Downloads
Velocity of Transverse Wave is the core string-wave speed block in Waves and Sound, and NEET uses it in direct formula and condition-change questions through the subtopic Wave Velocity in Stretched Strings. The anchor relation is v = sqrt(T/m), so speed increases with tension and decreases with linear density. The same idea is recast in equivalent forms like v = sqrt(T/(rho A)) = sqrt(S/rho), and many MCQs test whether students identify which quantity is held fixed before comparing cases. This topic also appears in applications where tension changes due to hanging load, buoyancy, or thermal stress, so dimensional discipline and condition reading are mandatory.
Formula-DrivenApplication MCQsNCERT-Aligned
Expected QuestionsQ
1
Typically appears as one direct or mixed formula-application question in Waves and Sound.
Time Required⏱
1.5 h
About 45 minutes for formula mapping and 45 minutes for condition-change numericals.
Difficulty⚡
Medium
Formula is short, but errors are frequent when students confuse mass, linear density, and material density.
NRI USA Curriculum GapUS
Moderate Bridge Needed
US high-school tracks often treat string waves conceptually, while NEET expects rapid switching among equivalent expressions and constraint-based comparisons.
5Subtopics
20Practice Questions
4Free Downloads
1.5 hPrep Time
Velocity of Transverse Wave Weightage and Trend
Waves and Sound - Topic 5| NEET Year | Questions from this Topic | Bar | Marks |
|---|---|---|---|
| 2020 | 0 | 0 | |
| 2021 | 1 | 4 | |
| 2022 | 0 | 0 | |
| 2023 | 0 | 0 | |
| 2024 | 1 | 4 | |
| 2025 | 0 | 0 | |
| Topic-linked asks in recent NEET papers | 2 | 8 |
Most asks check proportional reasoning from v = sqrt(T/m) after one parameter change.
Common mixed stems convert m = rho A and test whether students substitute correctly.
Advanced variants include effective tension under buoyancy or thermal stress before speed comparison.
Common mixed stems convert m = rho A and test whether students substitute correctly.
Advanced variants include effective tension under buoyancy or thermal stress before speed comparison.
0.3
Avg Questions / Year
8
Total Marks (6 yrs)
Mixed
Pattern
Medium
Difficulty
5-Step Accuracy Routine for String-Speed Questions
1
Lock the base relation first Start from v = sqrt(T/m) and write m as linear density only; never replace it directly by total mass without length context.
2
Check what stays constant Before comparing two cases, mark whether T, A, rho, or length is fixed; this determines whether speed varies as sqrt(T), 1/sqrt(rho), or 1/sqrt(A).
3
Choose the right equivalent form When stress or material data is given, switch to v = sqrt(S/rho) or v = sqrt(T/(rho A)) instead of forcing the original form.
4
Handle modified tension explicitly For hanging mass use T = Mg; for immersion use T = Mg(1 - sigma/rho); for thermal case use T = YAalphaDeltaTheta before substitution.
5
Finish with dimension and ratio checks Speed must remain in m/s and scale with square root factors; if a doubled tension gives doubled speed, the calculation is wrong because speed should scale by sqrt(2).
Velocity of Transverse Wave Download Kit
PDF · Cheat Sheet · MCQ Set · PYQFull Notes
Detailed notes on Wave Velocity in Stretched Strings with all textbook variants of tension and equivalent expressions.
Download PDFFormula Sheet
Compact sheet for v = sqrt(T/m), v = sqrt(T/(rho A)), v = sqrt(S/rho), and modified tension cases.
Download PDFMCQ Practice
Focused set on parameter-change numericals where one must identify the valid tension model before computing speed.
Download PDFPYQ Workbook
Chapter-level PYQ workbook with wave-speed and related wave-formula questions arranged by pattern and trap.
Download PDFSubtopics in Velocity of Transverse Wave
2-Column TableRapid Revision Cards
Concept → Trap → Example1) Wave Velocity in Stretched Strings
Core formulaThe velocity of a transverse wave in a stretched string is given by v = sqrt(T/m), where T is tension and m is linear density.
- Use m as mass per unit length; if area and material density are given, write m = rho A.
- For stress form, v = sqrt(S/rho) with S = T/A, useful when material properties are provided.
- Trap: replacing linear density with total mass directly, which breaks dimensions and gives wrong speed scaling.
Example (NEET-style)For T = 81 N and m = 9 x 10^-3 kg/m, speed is v = sqrt(81 / 0.009) = sqrt(9000) approximately 94.9 m/s. If tension becomes 4T with m unchanged, new speed is 2v, not 4v.
Curriculum Gap: India vs USA
Two concrete preparation gaps to bridge for NEET readinessAP Physics 1 conceptual wave treatment vs NEET equation switching
AP Physics 1 often emphasizes conceptual transverse-motion interpretation, but NEET frequently demands fast switching among equivalent speed forms based on given data.
- Practice converting among v = sqrt(T/m), v = sqrt(T/(rho A)), and v = sqrt(S/rho) in one minute drills.
- Build condition tables for what to do when tension source changes: load, immersion, or thermal expansion.
US problem sets vs NEET constraint-heavy MCQs
Many US textbook sets give one clean formula context, while NEET options are designed around hidden assumptions like constant length or changed effective tension.
- Train with ratio questions where only one parameter changes and verify square-root dependence.
- Add unit checks at every step so linear density and material density are never interchanged.
NEET-style practice questions
4 MCQs1A string has tension 64 N and linear density 4 x 10^-3 kg/m. The wave speed on the string is closest to:Wave Velocity in Stretched Strings
40 m/s
80 m/s
126 m/s
160 m/s
Use the governing relation for this subtopic: v = sqrt(T/m). Here T = 64 N and m = 4 x 10^-3 kg/m, so T/m = 64/0.004 = 16000. Therefore v = sqrt(16000) approximately 126.5 m/s, so 126 m/s is the best option. Option 80 m/s would correspond to using v proportional to T/m without square root. Option 160 m/s is another common mistake from rough doubling logic. Option 40 m/s comes from wrong handling of powers of ten in linear density. The key is to keep linear density in kg/m and apply square root at the end.
2For the same string length and material, tension is increased from T to 9T while linear density remains unchanged. The ratio of new to old wave speed is:Wave Velocity in Stretched Strings
9
3
1/3
sqrt(9/2)
From v = sqrt(T/m), if m is unchanged then speed varies as sqrt(T). Increasing tension from T to 9T gives v_new/v_old = sqrt(9T/T) = sqrt(9) = 3. Option 9 is the trap when students forget square-root dependence. Option 1/3 reverses the ratio and would apply only if tension reduced by factor 9. Option sqrt(9/2) incorrectly introduces a denominator not present in the condition. This type of question checks whether you identify the invariant quantity first and then apply proportionality correctly rather than substituting numbers unnecessarily.
3A wire of area A and material density rho carries tension T. Which expression gives transverse wave speed correctly in terms of these quantities?Wave Velocity in Stretched Strings
sqrt(TA/rho)
sqrt(T/(rho A))
sqrt(rho A/T)
T/(rho A)
Start from v = sqrt(T/m) and substitute linear density m = rho A. That gives v = sqrt(T/(rho A)). Option A puts area in numerator, which would increase speed with thicker wire at fixed tension, opposite to the formula. Option C is the reciprocal and has wrong dependence. Option D omits square root and has dimensions of velocity squared, not velocity. This question is a standard conversion trap in NEET-style papers: students may know v = sqrt(T/m) but lose marks while translating m into material parameters.
4A mass M hangs from a pulley and keeps a string under tension. If the load is immersed in a liquid of density sigma and load material density is rho, effective tension becomes T = Mg(1 - sigma/rho). Which statement is correct?Wave Velocity in Stretched Strings
Speed increases because buoyancy always increases tension
Speed remains unchanged because M is constant
Speed decreases because effective tension decreases
Speed becomes independent of linear density
The topic formula remains v = sqrt(T/m). Here immersion causes buoyant upthrust, reducing effective tension to Mg(1 - sigma/rho), which is smaller than Mg when sigma is positive and less than rho. Therefore v decreases if m is unchanged. Option A reverses buoyancy effect. Option B ignores that tension, not just mass value, governs speed. Option D is false because m remains in the denominator under square root in every case. This style checks if the student updates the physical model for tension before doing any substitution.
Practice Questions
Click "Reveal Answer" after attempting1A stretched string has linear density 2.5 x 10^-3 kg/m and wave speed 100 m/s. Find the tension in the string.
10 N
20 N
25 N
40 N
👁 Reveal Answer
Correct option: C (25 N). Use v = sqrt(T/m), so T = m v^2. Substituting m = 2.5 x 10^-3 kg/m and v = 100 m/s gives T = 2.5 x 10^-3 x 10^4 = 25 N. Option A and B come from arithmetic slips in powers of ten, while D comes from treating 2.5 x 10^-3 as 4 x 10^-3 incorrectly.
2For a wire with fixed material density rho and fixed tension T, cross-sectional area is doubled. New speed compared to old speed is:
2v
v/sqrt(2)
sqrt(2)v
v/2
👁 Reveal Answer
Correct option: B (v/sqrt(2)). Write v = sqrt(T/(rho A)). With T and rho fixed, v is inversely proportional to sqrt(A). If A becomes 2A, then v_new = v_old/sqrt(2). Option A assumes direct proportionality with area. Option C is sign-reversed dependence. Option D overestimates the reduction by using linear instead of square-root dependence.
3A string is loaded by a mass M = 4 kg. Its linear density is 0.01 kg/m. Take g = 10 m/s^2. Find wave speed.
20 m/s
40 m/s
63 m/s
80 m/s
👁 Reveal Answer
Correct option: C (63 m/s, approximately). First tension T = Mg = 4 x 10 = 40 N. Then v = sqrt(T/m) = sqrt(40/0.01) = sqrt(4000) approximately 63.2 m/s. Option B arises from forgetting the square root and simplifying too early. Option D comes from rounding 4000 to 6400 by mistake. Option A is far below expected value for this tension-density pair.
4If initial speed on a string is v and the linear density is increased to 4m while tension is reduced to T/4, the new speed is:
v
v/2
v/4
v/8
👁 Reveal Answer
Correct option: C (v/4). Since v is proportional to sqrt(T/m), the ratio becomes v_new/v_old = sqrt((T/4)/(4m)) = sqrt(T/(16m)) / sqrt(T/m) = 1/4. Option B is the usual trap when only one of the two changes is accounted for. Option A ignores both parameter changes. Option D applies an extra square-root reduction that is not present.
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Frequently Asked Questions
Notes · Downloads · Revision · Important QuestionsWhy does wave speed on a string depend on linear density and not directly on total mass?
The travelling disturbance interacts locally with each small segment of the string, so inertia enters as mass per unit length m, not as total mass of the entire string. In v = sqrt(T/m), doubling total length at the same m does not change local inertial resistance and therefore does not change speed. Students lose marks when they substitute whole mass without dividing by length.
When should I use v = sqrt(T/(rho A)) instead of v = sqrt(T/m)?
Use v = sqrt(T/(rho A)) whenever the question gives material density rho and cross-sectional area A rather than linear density directly. This is just the same relation with m = rho A substituted. It is not a different physical law. If you are given m already, the direct form is faster and reduces algebra mistakes in time-limited NEET conditions.
How do I decide whether speed increases or decreases without full calculation?
First identify the change in tension and linear density separately. Since v scales as sqrt(T/m), any multiplicative change in T increases speed by square root of that factor, while any increase in m decreases speed by square root. Build quick ratio expressions before plugging numbers. This avoids arithmetic errors and is often enough to eliminate three options immediately.
Why does immersion of the hanging load reduce wave speed?
Immersion introduces buoyant force upward on the load, reducing effective downward force and hence the string tension. The modified tension is T = Mg(1 - sigma/rho), which is smaller than Mg when sigma is less than rho but non-zero. Because speed depends on sqrt(T), reduced tension directly reduces speed. Many learners incorrectly assume adding liquid increases resistance and therefore tension.
What is the most common trap in NEET questions on this topic?
The most frequent trap is forgetting square-root dependence and using linear proportionality. For example, if tension becomes four times, speed becomes two times, not four times. A second trap is mixing material density rho with linear density m and treating them as the same unit. Always write units beside symbols before substitution to prevent this confusion.
In thermal-stress cases, which formula should be applied first?
Apply the tension model first: T = YAalphaDeltaTheta (as given in the textbook context), then substitute into v = sqrt(T/m). Students who start directly from v = sqrt(S/rho) without identifying available data often drop constants or misuse A. The safest sequence is: identify tension source, write T, then move to speed relation and simplify.
Can this topic be asked as part of another wave chapter question rather than directly?
Yes. NEET commonly embeds this relation inside standing-wave, frequency, or comparative wave-motion stems. You may be given a setup where frequency or wavelength changes and must infer whether speed changed due to tension or density variation. So treat v = sqrt(T/m) as a support formula that links many wave subtopics, not as an isolated definition question.
How much revision is enough before exam day for this topic?
One strong revision cycle should include formula map, three ratio-based checks, and at least six mixed MCQs involving tension modifications. Because the formula family is compact, gains come from condition recognition, not memorizing more theory. If you can solve load, immersion, and area-density conversion cases without re-deriving basics, your readiness for this block is usually sufficient.
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