Wave Equation — y = A sin(kx - ωt)
Waves & Sound
7
JEE Qs
8%
Hard
60
min
Master the sign conventions for wave direction and clearly distinguish between wave velocity and the oscillatory particle velocity for accurate problem-solving.
🧮 Key Formulas
✅ Key Points for JEE
- 1The sign in `kx ± ωt` determines the direction of wave propagation: `-` for +x direction, `+` for -x direction.
- 2The argument `(kx ± ωt + φ)` represents the phase of the wave, which remains constant for any given crest or trough moving through the medium.
- 3Wave speed (v) is the speed at which the disturbance propagates through the medium and is constant for a given medium, whereas particle speed (v_p) is the speed of an oscillating particle in the medium and varies sinusoidally.
- 4Particle velocity and acceleration are found by partial differentiation of `y(x,t)` with respect to time `t`, treating position `x` as a constant.
⚠️ Common Mistakes
- ✕Confusing wave velocity (v) with particle velocity (v_p) and their respective derivations.
- ✕Incorrectly identifying the direction of wave propagation due to misinterpretation of the `±` sign in the phase term `(kx ± ωt)`.
- ✕Errors in partial differentiation when calculating particle velocity or acceleration, especially sign errors or treating x as a variable during time differentiation.
- ✕Not understanding that `k` and `ω` are properties of the wave itself, while `A` describes the maximum displacement of the medium's particles.
📝 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