Waves

20 NEET-UG practice questions on Waves, part of Physics. The first 20 are below; the first 5 with answers and explanations (tap Show answer after you have chosen), the rest in Learn with a free account.

1. Question 1 · Easy

   Given below are two statements: Statement I: In a stationary wave, the distance between two adjacent nodes is one full wavelength. Statement II: An air column closed at one end supports only the odd harmonics of its fundamental. Choose the correct answer.

   1. AStatement I is correct but Statement II is incorrect
   2. BBoth Statement I and Statement II are correct
   3. CStatement I is incorrect but Statement II is correct
   4. DBoth Statement I and Statement II are incorrect

   Show answerHide answer

   Answer: C · Statement I is incorrect but Statement II is correct

   Adjacent nodes are λ/2 apart, so Statement I is false. A pipe closed at one end has a node at that end and an antinode at the open end, so only f, 3f, 5f and so on can fit, and Statement II is true.

   • A: This reverses the truth values of the two statements.
   • B: Statement I is false, since the spacing is λ/2.
   • D: Statement II is true: the closed pipe has only odd harmonics.

   Remember this

   Node to node is λ/2; node to adjacent antinode is λ/4.

2. Question 2 · Medium

   A string 1 m long of linear mass density 0.01 kg/m is fixed at both ends and kept under a tension of 100 N. What is the frequency of its third harmonic?

   1. A300 Hz
   2. B150 Hz
   3. C100 Hz
   4. D50 Hz

   Show answerHide answer

   Answer: B · 150 Hz

   Wave speed v = √(T/μ) = √(100/0.01) = 100 m/s. The fundamental is v/(2L) = 50 Hz, so the third harmonic is 3 × 50 = 150 Hz.

   • A: This uses v/L as the fundamental instead of v/(2L).
   • C: This is the second harmonic.
   • D: This is the fundamental, not the third harmonic.

   Remember this

   For a string fixed at both ends, fₙ = nv/(2L), with all harmonics present.

3. Question 3 · Hard

   In a resonance tube experiment with a 500 Hz tuning fork, the first resonance occurs at an air-column length of 16 cm and the second at 50 cm. What are the speed of sound and the end correction?

   1. A340 m/s and 2 cm
   2. B333 m/s and 1 cm
   3. C320 m/s and 0 cm
   4. D340 m/s and 1 cm

   Show answerHide answer

   Answer: D · 340 m/s and 1 cm

   The two lengths differ by λ/2: 50 − 16 = 34 cm, so λ = 68 cm and v = 500 × 0.68 = 340 m/s. The end correction e = (l₂ − 3l₁)/2 = (50 − 48)/2 = 1 cm. Check: l₁ + e = 17 cm = λ/4.

   • A: This omits the factor 1/2 in the end correction.
   • B: This uses v = (4/3)fl₂, ignoring the end correction.
   • C: This uses v = 4fl₁, ignoring the end correction.

   Remember this

   Using the difference of two resonance lengths removes the end correction from the speed.

4. Question 4 · Easy

   A wave on a string is given by y = 0.02 sin(4πt − 0.5πx), in SI units. What is its speed?

   1. A4 m/s
   2. B8 m/s
   3. C2 m/s
   4. D0.125 m/s

   Show answerHide answer

   Answer: B · 8 m/s

   Speed = ω/k = 4π/(0.5π) = 8 m/s. Check: f = 2 Hz and λ = 2π/k = 4 m, so fλ = 8 m/s.

   • A: This is the wavelength, 2π/k.
   • C: This is the frequency, ω/2π.
   • D: This inverts the ratio, using k/ω.

   Remember this

   For y = a sin(ωt − kx), v = ω/k, with the wave moving towards +x.

5. Question 5 · Medium

   Match List-I with List-II. The figure draws displacement patterns in four air columns, each 85 cm long, with the speed of sound 340 m/s. List-I (Pattern) A. Pipe A B. Pipe B C. Pipe C D. Pipe D List-II (Frequency) I. 100 Hz II. 200 Hz III. 300 Hz IV. 400 Hz

   

   −+Fit to screenClose

   

   1. AA-III, B-II, C-I, D-IV
   2. BA-I, B-II, C-III, D-IV
   3. CA-III, B-I, C-II, D-IV
   4. DA-IV, B-II, C-I, D-III

   Show answerHide answer

   Answer: A · A-III, B-II, C-I, D-IV

   For a closed pipe f₁ = v/4L = 340/3.4 = 100 Hz, and only odd harmonics occur: C is 100 Hz and A, with L = 3λ/4, is 300 Hz. For an open pipe f₁ = v/2L = 200 Hz: B is 200 Hz and D, the second harmonic, is 400 Hz.

   • B: Exchanges the closed-pipe third harmonic and fundamental.
   • C: Exchanges the fundamentals of the open and closed pipes.
   • D: Exchanges the patterns of pipes A and D.

   Remember this

   Closed pipe: L = (2n − 1)λ/4 with odd harmonics. Open pipe: L = nλ/2 with all harmonics.

6. Question 6 · Medium

   A snapshot of a transverse wave of frequency 50 Hz on a stretched string is plotted. If the string has linear mass density 0.01 kg/m, find its tension.

   

   −+Fit to screenClose

   

   1. A1 N
   2. B4 N
   3. C0.2 N
   4. D16 N

   Answer and explanation in LearnFree account

7. Question 7 · Medium

   Consider these statements about a stationary wave on a string. A. The distance between two adjacent nodes is λ/2. B. All particles between two adjacent nodes vibrate in the same phase. C. The wave carries energy along the string from one end to the other. D. Nodes are points that have zero displacement at all times. Which of the statements given above are correct?

   1. AB and C only
   2. BA and D only
   3. CA, C and D only
   4. DA, B and D only

   Answer and explanation in LearnFree account

8. Question 8 · Hard

   On a sonometer, the tension in a wire is increased by 44% and its vibrating length is reduced by 20%. By what percentage does its fundamental frequency change?

   1. AIncreases by 50%
   2. BIncreases by 20%
   3. CIncreases by 44%
   4. DIncreases by 80%

   Answer and explanation in LearnFree account

9. Question 9 · Easy

   Which harmonics are present in the stationary waves set up in an air column closed at one end?

   1. AOnly the even harmonics
   2. BOnly the odd harmonics
   3. CAll harmonics
   4. DOnly the fundamental

   Answer and explanation in LearnFree account

10. Question 10 · Medium

    When open at both ends, a pipe has a fundamental frequency of 300 Hz. One end is now closed. What is the new fundamental frequency? (Neglect end corrections.)

    1. A100 Hz
    2. B150 Hz
    3. C300 Hz
    4. D600 Hz

    Answer and explanation in LearnFree account

11. Question 11 · Hard

    Two successive resonant frequencies of an organ pipe are 425 Hz and 595 Hz. Taking the speed of sound in air as 340 m/s and neglecting end correction, which description fits the pipe?

    1. AOpen at both ends; length 2 m
    2. BClosed at one end; length 0.5 m
    3. COpen at both ends; length 1 m
    4. DClosed at one end; length 1 m

    Answer and explanation in LearnFree account

12. Question 12 · Medium

    A wave on a string is described by y = 0.02 sin(4πx − 200πt), with x and y in metres and t in seconds. What are its speed and direction of travel?

    1. A0.5 m/s, along +x
    2. B100 m/s, along +x
    3. C50 m/s, along +x
    4. D50 m/s, along −x

    Answer and explanation in LearnFree account

13. Question 13 · Medium

    Tuning fork A has a frequency of 320 Hz. Sounded with fork B, it gives 5 beats per second. When a little of fork B's prong is filed away, the beat frequency falls to 3 per second. What was the original frequency of B?

    1. A325 Hz
    2. B317 Hz
    3. C323 Hz
    4. D315 Hz

    Answer and explanation in LearnFree account

14. Question 14 · Easy

    Through which media can longitudinal mechanical waves travel?

    1. ASolids, liquids and gases
    2. BGases only
    3. CSolids only
    4. DSolids and liquids only

    Answer and explanation in LearnFree account

15. Question 15 · Medium

    Match List-I with List-II for the progressive wave y(x, t) = a sin(kx − ωt). List-I (quantity) A. Wave speed B. Wavelength C. Period D. Maximum speed of a particle of the medium List-II (expression) I. aω II. 2π/ω III. ω/k IV. 2π/k Choose the correct answer.

    1. AA-I, B-IV, C-II, D-III
    2. BA-III, B-II, C-IV, D-I
    3. CA-III, B-IV, C-II, D-I
    4. DA-II, B-IV, C-III, D-I

    Answer and explanation in LearnFree account

16. Question 16 · Easy

    In a stationary wave of wavelength λ, what is the distance between a node and the nearest antinode?

    1. Aλ/2
    2. Bλ
    3. Cλ/4
    4. D3λ/4

    Answer and explanation in LearnFree account

17. Question 17 · Medium

    The first overtone of a pipe of length 30 cm, closed at one end, has the same frequency as the fundamental of an open pipe. Neglecting end corrections, what is the length of the open pipe?

    1. A15 cm
    2. B45 cm
    3. C20 cm
    4. D60 cm

    Answer and explanation in LearnFree account

18. Question 18 · Medium

    A string fixed at both ends has two consecutive resonant frequencies of 420 Hz and 490 Hz. What is its fundamental frequency, and which harmonic is the 420 Hz mode?

    1. A70 Hz; the sixth harmonic
    2. B70 Hz; the seventh harmonic
    3. C35 Hz; the twelfth harmonic
    4. D140 Hz; the third harmonic

    Answer and explanation in LearnFree account

19. Question 19 · Hard

    A stationary wave on a string is y = (4 cm) sin(πx/15) cos(96πt), with x in cm and t in s. Consider the following statements: A. Adjacent nodes are 15 cm apart. B. The amplitude of vibration of the particle at x = 5 cm is 2 cm. C. Each of the two travelling waves that form it moves at 14.4 m/s. D. The frequency of vibration is 48 Hz. Which of these are correct?

    1. AA and C only
    2. BA, C and D only
    3. CA, B and C only
    4. DB, C and D only

    Answer and explanation in LearnFree account

20. Question 20 · Medium

    Two wires of the same material, one with twice the diameter of the other, are stretched with equal tensions. What is the ratio of the speed of transverse waves on the thinner wire to that on the thicker wire?

    1. A√2 : 1
    2. B1 : 2
    3. C4 : 1
    4. D2 : 1

    Answer and explanation in LearnFree account