Ch 6Superposition of Waves — Class 12 Physics, concept-first.

A wave is something you have already met in several everyday forms — water waves, sound waves, light waves — as well as under the broader headings mechanical waves and electromagnetic waves.

Picture the ripples that spread out on the surface of water when a stone is dropped into it. The water is displaced locally, right where the stone actually falls, and this disturbance slowly spreads o…

The properties of a progressive wave -- already established in Class XI, so only briefly recapped here as they will be used repeatedly through this chapter -- are: every particle of the medium execute…

REFLECTION is what happens when a progressive wave, travelling through one medium, reaches an interface with a second, different medium: part of the wave's energy is sent back into the original medium…

Consider a long, light string with one end (B) attached to a perfectly rigid support, representing the boundary between a rarer medium (the light string itself) and a denser medium (the immovable supp…

The same reflection rules apply to a LONGITUDINAL wave, expressed in terms of pressure regions instead of crest/trough shape -- a compression (a locally high-pressure region) plays the role of a crest…

The PRINCIPLE OF SUPERPOSITION OF WAVES states that, when two or more waves travelling through a medium pass through a common point at the same time, each wave produces its own displacement at that po…

Consider two wave pulses of EQUAL amplitude and the SAME phase (i.e. the same shape and orientation, e.g. both upward crests), launched from opposite ends of a string and approaching each other.

Now consider two wave pulses of the SAME (equal) amplitude but OPPOSITE phase -- for instance, one an upward crest and the other an equal-sized downward trough -- again launched from opposite ends of…

The two pulse examples above (6.4.1, 6.4.2) show the two EXTREME cases -- fully constructive and fully destructive interference.

Sections 6.4.1-6.4.3 examined superposition quite generally -- two wave PULSES moving in either the same or opposite senses, and then two continuous waves of the same frequency differing by an arbitra…

Imagine a string stretched between two fixed points; if it is pulled aside at the middle and released, it settles into a recognisable, fixed pattern of oscillation known as a stationary wave.

To derive the exact resultant displacement, consider two simple harmonic progressive waves of EQUAL amplitude a and wavelength , travelling along the x-axis in OPPOSITE directions: (Eq.

Gathering the results derived above, a stationary wave has the following properties. (1) It is produced by the superposition of two IDENTICAL waves (equal amplitude, equal frequency), of either kind (…

Bringing together the contrasts drawn out across sections 6.4-6.5.3, a progressive wave and a stationary wave differ in several fundamental ways.

Every object that is disturbed -- struck, plucked, or otherwise set into motion and then left alone -- tends to oscillate at one particular frequency of its own, called its NATURAL FREQUENCY.

A string or an air column, once set vibrating, reflects waves at its ends and can support stationary waves -- but only certain specific wavelengths (or, equivalently, frequencies) are actually possibl…

When an air column vibrates -- whether in a pipe closed at one end or open at both ends -- the boundary conditions require an ANTINODE to sit at every OPEN end (since the air there is comparatively fr…

Consider a long cylindrical tube, closed at one end, with a vibrating tuning fork held near its open end sending sound waves in.

Now consider a pipe OPEN at both ends, again excited by a tuning fork held near one end. Even with both ends open, the air inside the pipe is still confined by the tube's walls and is slightly denser…

The end correction e introduced in 6.7.1 can itself be measured experimentally, without needing to know the value of (the speed of sound) in advance, by comparing TWO pipes of the SAME diameter but di…

Exactly the same standing-wave reasoning used for air columns (sections 6.7.2, 6.7.3) applies to a stretched STRING of length l, linear density (mass per unit length) m, held under tension T between t…

The fundamental-frequency formula derived above, (Eq. 6.32), can be broken apart into three separate proportionality statements, each obtained by holding TWO of the three quantities (l, T, m) fixed an…

A SONOMETER is the standard laboratory apparatus for studying and verifying the three laws of a vibrating string.

BEATS are a further, distinctly audible consequence of the principle of superposition. When two sound waves of the SAME amplitude but SLIGHTLY DIFFERENT frequencies travel through a medium in the same…

Consider two sound waves of the SAME amplitude a but slightly different frequencies and , assumed (for simplicity) to arrive exactly in phase with each other at a chosen listening point x = 0: and .

The beats phenomenon has several genuinely practical applications. FIRST, musicians use beats to TUNE instruments to each other, or to a reference pitch: two notes are sounded together and adjusted (e…

Sound, once produced, is perceived by a listener through three distinct, subjective CHARACTERISTICS -- loudness, pitch, and quality -- even though, physically, sound itself is fully described by just…

Every audible musical sound ultimately originates from one of three kinds of vibrating source -- a stretched string, a column of air, or a stretched membrane/struck plate -- and musical instruments ar…

The chapter-end exercises of the Balbharati Physics Std-XII textbook for Superposition of Waves, in the book's own printed order: five multiple-choice questions, five short 'answer in brief' items, an…

Sample papers and previous-year board questions for this subject.