Doppler Effect — Moving source, moving observer
Waves & Sound
7
JEE Qs
8%
Hard
75
min
Master the sign convention for relative velocities of source, observer, and medium, as this is the most common pitfall in Doppler effect problems.
🧮 Key Formulas
✅ Key Points for JEE
- 1The Doppler effect depends on the relative motion between the source, the observer, and the medium. All velocities (source, observer, wind) must be considered relative to the medium for sound, not always relative to the ground.
- 2Careful application of the sign convention in the Doppler formula is crucial. A simple rule is to always think about whether the relative motion tends to increase or decrease the observed frequency/wavelength.
- 3When a medium (e.g., wind) is moving, the effective speed of sound relative to the ground changes. This effective speed must be used as `v_sound` in the formula, adjusted based on the wind's direction along the source-observer line.
- 4For reflection problems (e.g., sound reflecting off a wall), the problem should be broken into two stages: first, the wall acts as an observer receiving sound from the source; second, the wall acts as a source emitting the reflected sound to the actual observer.
- 5If the source or observer moves at an angle to the line joining them, only the components of their velocities along the line joining the source and observer are considered for the Doppler shift. This often involves `v_component = v * cos(theta)`.
⚠️ Common Mistakes
- ✕Incorrectly applying the sign convention for `v_observer` and `v_source` in the numerator and denominator, leading to inverted frequency shifts.
- ✕Neglecting the effect of a moving medium (wind) or incorrectly adding/subtracting its velocity from the speed of sound.
- ✕Misinterpreting the roles of source and observer in reflection scenarios, especially when dealing with moving reflecting surfaces, and not treating it as a two-step problem.
- ✕Not using the velocity component along the line joining source and observer when motion is angular, instead using the total speed.
📝 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 Part 2 Ch 15: Waves