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#	Question	Answer
1	What is the speed of electromagnetic waves in vacuum?	\( 2.99792458 \times 10^8 \) m s⁻¹.
2	Do electromagnetic waves require a medium for propagation?	No. They can travel through vacuum.
3	What is the wavelength of a wave?	The minimum distance between two points having the same phase.
4	Can longitudinal waves propagate in fluids?	Yes.
5	What is the speed of a longitudinal wave in a medium?	\( v = \sqrt{\frac{B}{\rho}} \).
6	A steel wire of mass \( 5.0 \times 10^{-3} \) kg and length 0.72 m is under a tension of 60 N. What is the speed of transverse waves on the wire?	93 m s⁻¹.
7	What is constructive interference?	When the phase difference between two waves is zero, the resultant amplitude is maximum (2a).
8	What is the amplitude of the resultant wave when two waves of amplitude a interfere with phase difference φ?	\( 2a \cos\frac{\phi}{2} \).
9	What is an antinode in a standing wave?	A point where the amplitude is maximum.
10	What are the frequencies of the normal modes of an air column closed at one end?	\( v = \left(n + \frac{1}{2}\right) \frac{v}{2L} \), where \( n = 0, 1, 2, 3, \dots \).
11	Two sitar strings produce beats of frequency 5 Hz. The frequency of one string is 427 Hz. What is the frequency of the other string?	422 Hz or 432 Hz.
12	What is the frequency of the resultant wave in beats?	The average of the two frequencies.
13	A bat emits ultrasonic sound of frequency 1000 kHz. What is the wavelength of the reflected sound if the speed of sound in air is 340 m s⁻¹?	3.4 × 10⁻⁴ m.
14	A wire of mass \( 3.5 \times 10^{-2} \) kg and linear density \( 4.0 \times 10^{-2} \) kg m⁻¹ vibrates in its fundamental mode at 45 Hz. What is the speed of the transverse wave?	78.75 m s⁻¹.
15	Two sitar strings produce beats of 6 Hz. The frequency of one is 324 Hz. After reducing tension, beats become 3 Hz. What is the frequency of the other string?	318 Hz.
16	What are capillary waves on water, and what restoring force produces them?	Ripples of fairly short wavelength (not more than a few centimetres); the restoring force is the surface tension of water.
17	What type of wave is produced by a motorboat sailing in water?	Transverse and longitudinal (a combination of both).
18	A wave is given by \( y(x,t) = 0.005\sin(80.0x - 3.0t) \) in SI units. What is the displacement y at \( x = 30.0 \) cm and \( t = 20 \) s?	Approximately 5 mm.
19	Why do sound waves travel faster in solids and liquids than in gases?	Although solids and liquids have higher mass densities than gases, their bulk (or Young's) modulus increases even more, so the overall speed \( v = \sqrt{B/\rho} \) is higher.
20	At a free (open) boundary, how does the net maximum displacement compare to the amplitude of the incident pulse?	It is twice the amplitude of each pulse (the incident and reflected pulses add in phase).
21	In a wave, what is actually transferred from one point to another?	Energy, not matter.
22	Using \( v = \sqrt{\gamma P / \rho} \), why is the speed of sound in air independent of pressure?	At constant temperature, P and ρ are directly proportional (from the ideal gas law), so P/ρ stays constant even as pressure changes.
23	A transverse harmonic wave on a string is \( y(x,t) = 3.0\sin(36t + 0.018x + \pi/4) \). Is it travelling or stationary, and if travelling, what are its speed and direction?	Travelling wave; speed = 20 m s⁻¹, moving in the negative x-direction.
24	For the travelling wave \( y(x,t) = 2.0\cos 2\pi(10t - 0.0080x + 0.35) \), what is the phase difference between two points separated by \( \lambda/2 \)?	\( \pi \) rad (180°).
25	For \( y(x,t) = 0.06\sin\left(\frac{2\pi}{3}x\right)\cos(120\pi t) \), what is the amplitude of oscillation at a point 0.375 m from one end?	≈ 0.0424 m (4.24 cm).
26	Why can we distinguish a violin note from a sitar note even when both have the same frequency?	Each instrument produces a different combination of harmonics (overtones) superposed on the fundamental, giving each note a distinct waveform/timbre even though the fundamental (pitch) frequency is the same.
27	Does a resonance tube — a glass tube partially filled with water — behave as a pipe open at both ends, or as a pipe closed at one end? (NEET 2024)	As a pipe closed at one end: the water surface is a node and the open top is an antinode.
28	Two successive (consecutive) resonant harmonics of a pipe closed at one end are 220 Hz and 260 Hz. What is the fundamental frequency of the pipe? (NEET 2017)	20 Hz (220 Hz and 260 Hz are the 11th and 13th harmonics, which differ by \( 2\nu_1 \)).
29	A pipe closed at one end is 85 cm long, with the speed of sound in air as 340 m s⁻¹. How many of its natural oscillation frequencies lie below 1250 Hz? (NEET 2014)	6 (fundamental = 100 Hz; the odd harmonics 100, 300, 500, 700, 900, 1100 Hz are all below 1250 Hz).
30	A travelling wave is given by \( y = C\sin\left[\frac{2\pi}{\lambda}(at - x)\right] \). What is its frequency? (NEET 2024)	\( \nu = \frac{a}{\lambda} \).