Waves for NEET UG
A wave carries energy from place to place without carrying matter along. This chapter covers wave speed, standing waves in strings and pipes, beats and the Doppler effect.
PhysicsClass 1162 MCQs3 lessons11 flashcards3 memory tricks
What you'll learn
- Wave basics and wave speed
Use v = fλ and the formulas for wave speed in strings and gases. - Standing waves in strings and pipes
Find the harmonics of a string, an open pipe and a closed pipe. - Beats and the Doppler effect
Find beat frequency and the apparent frequency heard when source or listener moves.
Key formulas
| Wave equation | v = fλ |
|---|---|
| Wave on a string | v = √(T/μ), μ = mass per unit length |
| Sound in a gas (Laplace) | v = √(γP/ρ) |
| Travelling wave | y = A sin(kx − ωt), k = 2π/λ |
| Beat frequency | f_beat = |f₁ − f₂| |
| Doppler effect (sound) | f' = f (v + v_o)/(v − v_s), for listener and source approaching each other |
Memory tricks
A pipe open at both ends (like a flute) gives all harmonics, f = nv/2L. A pipe closed at one end gives only odd harmonics, f = (2n − 1)v/4L.
When source and listener approach each other the heard frequency rises; when they move apart it falls.
Beat frequency = |f₁ − f₂|. Hearing 3 wows per second means the frequencies differ by 3 Hz.
Try 3 NEET-style questions
Q1. A string under a tension of 100 N has a linear mass density of 0.01 kg/m. The speed of transverse waves on it is
- 10 m/s
- 100 m/s
- 1000 m/s
- 1 m/s
Show answer
Answer: (2) 100 m/s
v = √(T/μ) = √(100/0.01) = √10⁴ = 100 m/s.
Q2. Two waves of the same frequency and equal amplitude A superpose in phase at a point. By the principle of superposition, the resultant amplitude is
- A
- 0
- A√2
- 2A
Show answer
Answer: (4) 2A
In phase, the crests coincide and the amplitudes add: A + A = 2A (constructive interference).
Q3. An organ pipe closed at one end can produce
- all harmonics of the fundamental
- only the even harmonics
- only the odd harmonics
- only the fundamental frequency
Show answer
Answer: (3) only the odd harmonics
The closed end must be a node and the open end an antinode, so the length holds an odd number of quarter wavelengths. The frequencies are f, 3f, 5f… — only odd harmonics.
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