Speed of Sound — Newton's formula, Laplace correction
Waves & Sound
7
JEE Qs
8%
Hard
60
min
Thoroughly understand the conditions (isothermal vs. adiabatic) and the factors affecting the speed of sound, particularly the independence from pressure and dependence on temperature and humidity.
🧮 Key Formulas
✅ Key Points for JEE
- 1Sound propagation is an adiabatic process, not isothermal. This is due to rapid compressions and rarefactions, leaving no time for heat exchange with the surroundings.
- 2Newton's formula (isothermal) gives a value lower than the experimental speed because it assumes constant temperature, which is incorrect.
- 3Laplace's correction (adiabatic) accounts for the heat generated during compression and absorbed during rarefaction, using the adiabatic bulk modulus `γP`.
- 4The speed of sound in a gas is directly proportional to the square root of its absolute temperature (`T` in Kelvin) and the adiabatic index (`γ`).
- 5The speed of sound in a gas is independent of pressure at a constant temperature, as density `ρ` changes proportionally with pressure `P` (maintaining `P/ρ` constant).
- 6Humidity increases the speed of sound because moist air is less dense (has a lower average molar mass) than dry air at the same temperature and pressure.
⚠️ Common Mistakes
- ✕Confusing isothermal and adiabatic conditions for sound propagation; mistakenly using Newton's formula or bulk modulus for isothermal changes.
- ✕Believing that the speed of sound in a gas depends on pressure when temperature is constant. It depends on `P/ρ`, and `P/ρ` is constant for an ideal gas at constant T.
- ✕Not converting temperature to Kelvin when using the formula `v = sqrt(γRT/M)`.
📝 Practice Questions
See allQ27.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: A sound wave has higher speed in solids than gases. Reason R: Gases have higher value of Bulk modulus than solids. In the light of the above statements, choose the correct answer from the options given below ⎪ ⎪ 2025 (28 Jan Shift 1) JEE Main Previous Year Paper (1) Both A and R are true but R is NOT the correct (2) A is true but R is false explanation of A (3) A is false but R is true (4) Both A and R are true and R is the correct explanation of A
Q40.Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The binding energy per nucleon is found to be practically independent of the atomic number A, for nuclei with mass numbers between 30 and 170. Reason (R): Nuclear force is long range. In the light of the above statements, choose the correct answer from the options given below : (1) (A) is true but (R) is false (2) (A) is false but (R) is true (3) Both (A) and (R) are true and (R) is the correct (4) Both (A) and (R) are true but (R) is NOT the explanation of (A) correct explanation of (A)
Q36.A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities ρ1 and ρ2′ , respectively. The frequency of 9th harmonic of closed tube is identical with 4th harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is ρ1 : ρ2 = 1 : 16, then the length of the open tube is : (1) 15 7 cm (2) 207 cm (3) 15 9 cm (4) 209 cm
Q24.A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is ( a−1a ) then the value of a is ________ → 2^i+6^j+8^k 2^i+^j+^k . The
Q24.Two open organ pipes of lengths 60 cm and 90 cm resonate at 6th and 5th harmonics respectively. The difference of frequencies for the given modes is _______ Hz . (Velocity of sound in air = 333 m/s )
Q2. The equation of stationary wave is : y = 2a sin ( 2πntλ ) cos ( 2πxλ ). Which of the following is NOT correct : (1) The dimensions of n/λ is [T] (2) The dimensions of n is [LT−1] (3) The dimensions of x is [L] (4) The dimensions of nt is [L]
NCERT Chapters
- Class 11 Physics Ch 15: Waves
- Class 11 Physics Ch 12: Thermodynamics