Beats — Beat frequency
Waves & Sound
7
JEE Qs
8%
Hard
40
min
Master the application of beat frequency to determine unknown frequencies, especially when one source is slightly altered (e.g., loaded or filed tuning fork), by carefully considering whether the alteration increases or decreases its original frequency.
🧮 Key Formulas
✅ Key Points for JEE
- 1Beats arise from the superposition of two sound waves of slightly different frequencies traveling in the same direction.
- 2The resultant wave's amplitude varies periodically with time, leading to periodic variations in the perceived loudness (intensity) of sound.
- 3Beat frequency (f_beat) is defined as the number of maxima (or minima) of sound intensity heard per second.
- 4For beats to be audible, the frequency difference between the two sources must be small, typically less than 10-12 Hz.
- 5Beats are a powerful tool for determining an unknown frequency by listening to the beats produced with a known standard frequency, or for tuning musical instruments (zero beats imply frequencies are matched).
⚠️ Common Mistakes
- ✕Forgetting to take the absolute difference for beat frequency, `f_beat = |f1 - f2|`.
- ✕Incorrectly determining the unknown frequency (e.g., choosing `f_known + f_beat` vs `f_known - f_beat`) without considering the physical effect of loading/filing a tuning fork or other source modifications.
- ✕Confusing beat frequency with the average frequency `(f1 + f2)/2` or the individual frequencies of the sources.
📝 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