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NCERT Solutions › Physics › Chapter 15

Chapter 15: Waves

NCERT Solutions for CBSE Class 10 Physics — 105 solved questions with detailed explanations.

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Solved Questions

Q1. The speed of a transverse wave on a string of mass per unit length μ under tension T is:

Difficulty: Easy · Topic: Wave Speed

Solution

v = √(T/μ), where T is tension and μ is mass per unit length.

Q2. In a stationary wave, the distance between a node and the nearest antinode is:

Difficulty: Easy · Topic: Stationary Waves

Solution

Distance between consecutive node and antinode = λ/4.

Q3. Two sound waves of frequencies 256 Hz and 260 Hz are sounded together. The beat frequency is:

Difficulty: Easy · Topic: Beats

Solution

Beat frequency = |f₁ - f₂| = |256 - 260| = 4 Hz.

Q4. Two tuning forks of frequencies 256 Hz and 260 Hz are sounded together. The beat frequency is:

Difficulty: Easy · Topic: Beats

Solution

Beat frequency = |f₁-f₂| = |256-260| = 4 Hz.

Q5. Two tuning forks of frequencies 440 Hz and 444 Hz are sounded together. The beat frequency is:

Difficulty: Easy · Topic: Beats

Solution

Beat frequency = |f₁-f₂| = |440-444| = 4 Hz.

Q6. Two tuning forks of frequencies 512 Hz and 516 Hz are sounded together. The beat frequency is:

Difficulty: Easy · Topic: Beats

Solution

Beat frequency = |f₁-f₂| = |512-516| = 4 Hz.

Q7. Two tuning forks of frequencies 300 Hz and 303 Hz are sounded together. The beat frequency is:

Difficulty: Easy · Topic: Beats

Solution

Beat frequency = |f₁-f₂| = |300-303| = 3 Hz.

Q8. Two tuning forks of frequencies 200 Hz and 205 Hz are sounded together. The beat frequency is:

Difficulty: Easy · Topic: Beats

Solution

Beat frequency = |f₁-f₂| = |200-205| = 5 Hz.

Q9. Forks 200Hz and 201Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|200-201|=1 Hz.

Q10. Forks 200Hz and 202Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|200-202|=2 Hz.

Q11. Forks 200Hz and 203Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|200-203|=3 Hz.

Q12. Forks 200Hz and 204Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|200-204|=4 Hz.

Q13. Forks 200Hz and 205Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|200-205|=5 Hz.

Q14. Forks 200Hz and 206Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|200-206|=6 Hz.

Q15. Forks 200Hz and 207Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|200-207|=7 Hz.

Q16. Forks 200Hz and 208Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|200-208|=8 Hz.

Q17. Forks 210Hz and 211Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|210-211|=1 Hz.

Q18. Forks 210Hz and 212Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|210-212|=2 Hz.

Q19. Forks 210Hz and 213Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|210-213|=3 Hz.

Q20. Forks 210Hz and 214Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|210-214|=4 Hz.

Q21. Forks 210Hz and 215Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|210-215|=5 Hz.

Q22. Forks 210Hz and 216Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|210-216|=6 Hz.

Q23. Forks 210Hz and 217Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|210-217|=7 Hz.

Q24. Forks 210Hz and 218Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|210-218|=8 Hz.

Q25. Forks 220Hz and 221Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|220-221|=1 Hz.

Q26. Forks 220Hz and 222Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|220-222|=2 Hz.

Q27. Forks 220Hz and 223Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|220-223|=3 Hz.

Q28. Forks 220Hz and 224Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|220-224|=4 Hz.

Q29. Forks 220Hz and 225Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|220-225|=5 Hz.

Q30. Forks 220Hz and 226Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|220-226|=6 Hz.

Q31. Forks 220Hz and 227Hz. Beat frequency:

Difficulty: Easy · Topic: Beats

Solution

|220-227|=7 Hz.

Q32. The frequency of the third harmonic of a closed organ pipe of length L is:

Difficulty: Easy-Medium · Topic: Standing Waves

Solution

Closed pipe has only odd harmonics. Third harmonic: f₃ = 3v/(4L).

Q33. The Doppler effect formula for the apparent frequency when source moves toward a stationary observer is:

Difficulty: Easy-Medium · Topic: Doppler Effect

Solution

When source moves toward stationary observer: f' = fv/(v - v_s). Frequency increases.

Q34. The speed of a transverse wave on a string (tension=10 N, linear density=0.01 kg/m) is:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ) = √(10/0.01) = 31.62 m/s.

Q35. The speed of a transverse wave on a string (tension=20 N, linear density=0.05 kg/m) is:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ) = √(20/0.05) = 20.0 m/s.

Q36. The speed of a transverse wave on a string (tension=40 N, linear density=0.1 kg/m) is:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ) = √(40/0.1) = 20.0 m/s.

Q37. The speed of a transverse wave on a string (tension=100 N, linear density=0.04 kg/m) is:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ) = √(100/0.04) = 50.0 m/s.

Q38. The speed of a transverse wave on a string (tension=50 N, linear density=0.02 kg/m) is:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ) = √(50/0.02) = 50.0 m/s.

Q39. The fundamental frequency of an open organ pipe of length L is:

Difficulty: Easy-Medium · Topic: Standing Waves

Solution

For an open organ pipe, fundamental frequency = v/(2L).

Q40. The second harmonic of an open organ pipe of length L is:

Difficulty: Easy-Medium · Topic: Standing Waves

Solution

For an open organ pipe, second harmonic = v/L.

Q41. The fundamental frequency of an closed organ pipe of length L is:

Difficulty: Easy-Medium · Topic: Standing Waves

Solution

For an closed organ pipe, fundamental frequency = v/(4L).

Q42. The third harmonic of an closed organ pipe of length L is:

Difficulty: Easy-Medium · Topic: Standing Waves

Solution

For an closed organ pipe, third harmonic = 3v/(4L).

Q43. The fifth harmonic of an closed organ pipe of length L is:

Difficulty: Easy-Medium · Topic: Standing Waves

Solution

For an closed organ pipe, fifth harmonic = 5v/(4L).

Q44. A string (tension 10 N, μ=0.010 kg/m) has wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ).

Q45. A string (tension 15 N, μ=0.015 kg/m) has wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ).

Q46. A string (tension 20 N, μ=0.020 kg/m) has wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ).

Q47. A string (tension 25 N, μ=0.025 kg/m) has wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ).

Q48. A string (tension 30 N, μ=0.030 kg/m) has wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ).

Q49. A string (tension 35 N, μ=0.035 kg/m) has wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ).

Q50. A string (tension 40 N, μ=0.040 kg/m) has wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ).

Q51. A string (tension 45 N, μ=0.045 kg/m) has wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ).

Q52. A string (tension 50 N, μ=0.050 kg/m) has wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ).

Q53. A string (tension 55 N, μ=0.055 kg/m) has wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ).

Q54. A string (tension 60 N, μ=0.060 kg/m) has wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ).

Q55. A string (tension 65 N, μ=0.065 kg/m) has wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ).

Q56. A string (tension 70 N, μ=0.070 kg/m) has wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ).

Q57. A string (tension 75 N, μ=0.075 kg/m) has wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ).

Q58. A string (tension 80 N, μ=0.080 kg/m) has wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ).

Q59. A string (tension 85 N, μ=0.085 kg/m) has wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ).

Q60. A string (tension 90 N, μ=0.090 kg/m) has wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ).

Q61. A string (tension 95 N, μ=0.095 kg/m) has wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ).

Q62. A string (tension 100 N, μ=0.100 kg/m) has wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ).

Q63. A string (tension 105 N, μ=0.105 kg/m) has wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v = √(T/μ).

Q64. String: T=5N, μ=0.005kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=31.62 m/s.

Q65. String: T=5N, μ=0.01kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=22.36 m/s.

Q66. String: T=5N, μ=0.02kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=15.81 m/s.

Q67. String: T=5N, μ=0.04kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=11.18 m/s.

Q68. String: T=5N, μ=0.05kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=10.0 m/s.

Q69. String: T=5N, μ=0.1kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=7.07 m/s.

Q70. String: T=10N, μ=0.005kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=44.72 m/s.

Q71. String: T=10N, μ=0.01kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=31.62 m/s.

Q72. String: T=10N, μ=0.02kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=22.36 m/s.

Q73. String: T=10N, μ=0.04kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=15.81 m/s.

Q74. String: T=10N, μ=0.05kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=14.14 m/s.

Q75. String: T=10N, μ=0.1kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=10.0 m/s.

Q76. String: T=20N, μ=0.005kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=63.25 m/s.

Q77. String: T=20N, μ=0.01kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=44.72 m/s.

Q78. String: T=20N, μ=0.02kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=31.62 m/s.

Q79. String: T=20N, μ=0.04kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=22.36 m/s.

Q80. String: T=20N, μ=0.05kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=20.0 m/s.

Q81. String: T=20N, μ=0.1kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=14.14 m/s.

Q82. String: T=40N, μ=0.005kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=89.44 m/s.

Q83. String: T=40N, μ=0.01kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=63.25 m/s.

Q84. String: T=40N, μ=0.02kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=44.72 m/s.

Q85. String: T=40N, μ=0.04kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=31.62 m/s.

Q86. String: T=40N, μ=0.05kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=28.28 m/s.

Q87. String: T=40N, μ=0.1kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=20.0 m/s.

Q88. String: T=50N, μ=0.005kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=100.0 m/s.

Q89. String: T=50N, μ=0.01kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=70.71 m/s.

Q90. String: T=50N, μ=0.02kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=50.0 m/s.

Q91. String: T=50N, μ=0.04kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=35.36 m/s.

Q92. String: T=50N, μ=0.05kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=31.62 m/s.

Q93. String: T=50N, μ=0.1kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=22.36 m/s.

Q94. String: T=80N, μ=0.005kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=126.49 m/s.

Q95. String: T=80N, μ=0.01kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=89.44 m/s.

Q96. String: T=80N, μ=0.02kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=63.25 m/s.

Q97. String: T=80N, μ=0.04kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=44.72 m/s.

Q98. String: T=80N, μ=0.05kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=40.0 m/s.

Q99. String: T=80N, μ=0.1kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=28.28 m/s.

Q100. String: T=100N, μ=0.005kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=141.42 m/s.

Q101. String: T=100N, μ=0.01kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=100.0 m/s.

Q102. String: T=100N, μ=0.02kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=70.71 m/s.

Q103. String: T=100N, μ=0.04kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=50.0 m/s.

Q104. String: T=100N, μ=0.05kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=44.72 m/s.

Q105. String: T=100N, μ=0.1kg/m. Wave speed:

Difficulty: Easy-Medium · Topic: Wave Speed

Solution

v=√(T/μ)=31.62 m/s.

Other Chapters in Physics

Ch 1: Physical WorldCh 2: Units & MeasurementsCh 3: Motion in a Straight LineCh 4: Motion in a PlaneCh 5: Laws of MotionCh 6: Work Energy & PowerCh 7: System of ParticlesCh 8: GravitationCh 9: Mechanical Properties of SolidsCh 10: Mechanical Properties of FluidsCh 11: Thermal Properties of MatterCh 12: ThermodynamicsCh 13: Kinetic TheoryCh 14: Oscillations

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