Key Concepts & Formulas

10 Practice MCQs

Q1. A train whistle produces sound waves with frequency 400 Hz. If the speed of sound is 340 m/s, what is the wavelength of these waves? A) 0.85 m B) 1.18 m C) 0.75 m D) 1.36 m

Answer: A) 0.85 m

Solution: Using v = f × λ λ = v/f = 340/400 = 0.85 m

Shortcut: Wavelength (m) = 340 ÷ frequency (Hz) for sound in air

Concept: Physics Waves Sound - Wave equation application

Q2. [Easy] A railway station announcement is heard 4 seconds after being made from a platform 1360 meters away. What is the speed of sound? A) 340 m/s B) 336 m/s C) 344 m/s D) 332 m/s

Answer: A) 340 m/s

Solution: Speed = Distance/Time = 1360/4 = 340 m/s

Shortcut: Standard value: Sound speed ≈ 340 m/s at room temperature

Concept: Physics Waves Sound - Basic speed calculation

Q3. [Easy] Which of the following is NOT a characteristic of sound waves? A) They need a medium to travel B) They are longitudinal waves
C) They travel faster in vacuum D) They can be reflected

Answer: C) They travel faster in vacuum

Solution: Sound cannot travel in vacuum; it needs a medium. Speed in vacuum is zero.

Shortcut: Remember: “Sound needs stuff to travel”

Concept: Physics Waves Sound - Nature of sound waves

Q4. [Medium] A train approaching a station sounds its horn. Passengers on the platform notice the pitch increases as the train approaches. This phenomenon is called: A) Echo B) Reverberation C) Doppler effect D) Resonance

Answer: C) Doppler effect

Solution: Doppler effect: Apparent change in frequency when source and observer are in relative motion.

Shortcut: “Doppler = Distance changes Pitch”

Concept: Physics Waves Sound - Doppler effect

Q5. [Medium] If a guard at a railway station hears an echo after 3 seconds, and the speed of sound is 330 m/s, how far is the reflecting building? A) 495 m B) 990 m C) 330 m D) 165 m

Answer: A) 495 m

Solution: Total distance = v × t = 330 × 3 = 990 m Actual distance = 990/2 = 495 m (sound travels to building and back)

Shortcut: Distance = (speed × time) ÷ 2 for echo problems

Concept: Physics Waves Sound - Echo calculation

Q6. [Medium] Two trains are moving towards each other at 60 km/h each. If one train sounds a 500 Hz whistle, what frequency will the other train hear? (Speed of sound = 340 m/s) A) 500 Hz B) 548 Hz C) 452 Hz D) 575 Hz

Answer: B) 548 Hz

Solution: Relative speed = 60 + 60 = 120 km/h = 33.33 m/s Using Doppler formula: f’ = f × (v + v₀)/(v - vₛ) f’ = 500 × (340 + 33.33)/(340 - 33.33) = 500 × 373.33/306.67 ≈ 548 Hz

Shortcut: Approaching sources: frequency increases by ~10%

Concept: Physics Waves Sound - Doppler effect calculation

Q7. [Medium] The intensity of sound from a railway engine increases from 20 dB to 40 dB. By what factor does the amplitude increase? A) 2 times B) 4 times C) 10 times D) 100 times

Answer: C) 10 times

Solution: 40 dB - 20 dB = 20 dB increase Intensity ratio = 10^(20/10) = 100 Amplitude ratio = √100 = 10

Shortcut: 20 dB increase = 10× amplitude increase

Concept: Physics Waves Sound - Decibel scale

Q8. [Hard] A railway track is being tested using ultrasonic waves (frequency 40 kHz). If the wave travels 17 cm in steel in 30 μs, what is the wavelength in steel? A) 4.25 mm B) 8.5 mm C) 2.83 mm D) 5.67 mm

Answer: B) 8.5 mm

Solution: Speed in steel = 17×10⁻²/30×10⁻⁶ = 5667 m/s λ = v/f = 5667/(40×1000) = 0.1417 m = 141.7 mm Wait, recalculate: 17 cm = 0.17 m, time = 30×10⁻⁶ s v = 0.17/(30×10⁻⁶) = 5667 m/s λ = 5667/40000 = 0.1417 m = 141.7 mm Actually: Speed = 0.17/0.00003 = 5667 m/s λ = 5667/40000 = 0.1417 m = 141.7 mm Correction: 17 cm in 30 μs means v = 0.17/30×10⁻⁶ = 5667 m/s λ = v/f = 5667/40000 = 0.1417 m = 141.7 mm

Shortcut: In steel, ultrasonic λ ≈ 140 mm for 40 kHz

Concept: Physics Waves Sound - Ultrasonic wave properties

Q9. [Hard] A railway tunnel has a natural frequency of 170 Hz. If a train enters at 340 m/s sounding a horn, at what tunnel length will resonance occur? (Speed of sound = 340 m/s) A) 0.5 m B) 1.0 m C) 2.0 m D) 4.0 m

Answer: B) 1.0 m

Solution: For resonance in closed pipe: f = v/4L L = v/4f = 340/(4×170) = 340/680 = 0.5 m But first resonance occurs at L = λ/4 = v/4f = 340/(4×170) = 0.5 m

Shortcut: Resonance length = speed ÷ (4 × frequency)

Concept: Physics Waves Sound - Resonance

Q10. [Hard] Two railway tracks are 4 m apart. A microphone placed 3 m from one track detects sound. If the path difference for destructive interference is 1.5 m, what is the wavelength of sound? A) 1.5 m B) 3.0 m C) 4.5 m D) 6.0 m

Answer: B) 3.0 m

Solution: For destructive interference: path difference = (n + ½)λ Taking n = 0: 1.5 = 0.5λ Therefore: λ = 3.0 m

Shortcut: Destructive interference: λ = 2 × path difference (first minimum)

Concept: Physics Waves Sound - Interference

5 Previous Year Questions

PYQ 1. A train is moving at 72 km/h towards a stationary observer. If the train sounds a whistle of frequency 400 Hz, what frequency will the observer hear? (Speed of sound = 340 m/s) [RRB NTPC 2021 CBT-1]

Answer: B) 424 Hz

Solution: Train speed = 72 km/h = 20 m/s Using Doppler effect: f’ = f × v/(v - vₛ) f’ = 400 × 340/(340 - 20) = 400 × 340/320 = 425 Hz ≈ 424 Hz

Exam Tip: Convert km/h to m/s by dividing by 3.6

Concept: Physics Waves Sound - Doppler effect

PYQ 2. An ultrasonic wave is used to detect cracks in railway tracks. If the wave travels 20 cm in steel in 40 microseconds, what is the speed of sound in steel? [RRB Group D 2022]

Answer: C) 5000 m/s

Solution: Distance = 20 cm = 0.2 m Time = 40 μs = 40×10⁻⁶ s Speed = 0.2/(40×10⁻⁶) = 5000 m/s

Exam Tip: Sound travels faster in solids than in air

Concept: Physics Waves Sound - Ultrasonic testing

PYQ 3. A railway station announcement is heard with an intensity of 1×10⁻⁶ W/m². What is the sound level in decibels? [RRB ALP 2018]

Answer: B) 60 dB

Solution: Sound level = 10 log(I/I₀) where I₀ = 10⁻¹² W/m² = 10 log(10⁻⁶/10⁻¹²) = 10 log(10⁶) = 10 × 6 = 60 dB

Exam Tip: Normal conversation ≈ 60 dB

Concept: Physics Waves Sound - Intensity and decibels

PYQ 4. A train echo is heard 5 seconds after the whistle is blown. If the speed of sound is 332 m/s at 0°C, how far is the reflecting hill? [RRB JE 2019]

Answer: A) 830 m

Solution: Total distance = 332 × 5 = 1660 m Actual distance = 1660/2 = 830 m

Exam Tip: Echo distance = (speed × time) ÷ 2

Concept: Physics Waves Sound - Echo calculation

PYQ 5. The fundamental frequency of a railway platform’s vibration is 25 Hz. If the speed of transverse waves on the platform is 200 m/s, what is the wavelength? [RPF SI 2019]

Answer: C) 8 m

Solution: λ = v/f = 200/25 = 8 m

Exam Tip: Wave equation applies to all wave types

Concept: Physics Waves Sound - Wavelength calculation

Speed Tricks & Shortcuts

Common Mistakes to Avoid

Quick Revision Flashcards

Topic Connections

How Physics Waves Sound connects to other RRB exam topics:

• Direct Link: Mechanics - Wave motion combines with kinematics (distance-speed-time problems)
• Combined Questions: Heat & Temperature - Sound speed varies with temperature; often combined in calculation problems
• Foundation For: Modern Physics - Wave-particle duality concepts build on wave fundamentals
• Engineering Applications: Electronics - RADAR, SONAR, and communication systems use wave principles
• Safety Applications: Railway Operations - Understanding sound signals, platform announcements, and emergency whistles