Physics · Class 12 Science
Ch 1Waves — Class 12 Physics, concept-first.
The previous chapter dealt with objects oscillating in isolation — a mass on a spring, a simple pendulum. But what happens when many such oscillators are connected together? A material medium is exactly that: a collection of particles bound by elastic forces, where the motion of one particle affects its neighbours.
Key concepts
Hover a concept to preview it and jump to its most relevant Q&A.
Wave Type Classification
Imagine you're standing at the edge of a still pond. You drop a pebble. Ripples spread outward in circles. Now imagine you're holding one end of a long rope tied to a wall.
Most relevant Q&A
- Given below are some examples of wave motion. State in each case if the wave motion is transverse, longitudinal or a combination of both: (a…Preview
- A wave travelling along a string is described by, $$y(x, t) = 0.005 \sin(80.0\,x - 3.0\,t),$$ in which the numerical constants are in SI uni…Preview
- You have learnt that a travelling wave in one dimension is represented by a function $y = f(x, t)$ where $x$ and $t$ must appear in the comb…Preview
- A transverse harmonic wave on a string is described by $$y(x, t) = 3.0 \sin(36\,t + 0.018\,x + \pi/4)$$ where $x$ and $y$ are in cm and $t$…Preview
- For the wave described in Exercise 14.8, plot the displacement ($y$) versus ($t$) graphs for $x = 0$, $2$ and $4\ \text{cm}$. What are the s…Preview
In previous exams
How often this chapter’s concepts have been examined — real appearance data, never estimated.
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Introduction
The previous chapter dealt with objects oscillating in isolation — a mass on a spring, a simple pendulum.
Transverse and Longitudinal Waves
When a disturbance travels through a medium, the particles of the medium oscillate about their mean positions.
Displacement Relation in a Progressive Wave
A progressive wave (also called a travelling wave) carries energy from one point to another without any bulk transfer of matter.
Amplitude and Phase
A progressive wave carries energy and information as it travels. To describe it fully, we need two numbers at every point: how big the disturbance is (the amplitude) and where in its cycle the disturb…
Wavelength and Angular Wave Number
A wave travelling through a medium carries energy and momentum, but what exactly do we mean by the "displacement" of a wave? For a wave on a string, the displacement is simply how far a particular poi…
Period, Angular Frequency and Frequency
A wave travelling through a medium carries energy and momentum, but what exactly do we mean by "the wave" at a given instant? The answer lies in the displacement of each particle of the medium from it…
The Speed of a Travelling Wave
When a wave travels through a medium, each particle of the medium oscillates about its mean position. The disturbance — the wave itself — moves forward at a definite speed.
Speed of a Transverse Wave on Stretched String
A wave travelling along a stretched string is a classic example of a transverse mechanical wave. The speed of such a wave is not arbitrary — it is determined entirely by two properties of the string:…
Speed of a Longitudinal Wave (Speed of Sound)
We now turn to the speed of a longitudinal wave — a wave in which the particles of the medium oscillate parallel to the direction of wave propagation.
The Principle of Superposition of Waves
When two or more waves travel through the same medium at the same time, the displacement of any particle of the medium is the vector sum of the displacements that the individual waves would produce in…
Reflection of Waves
When a wave travelling through a medium encounters a boundary — a point where the medium changes — part or all of the wave is reflected.
Standing Waves and Normal Modes
When a wave reflects from two boundaries — as in a string fixed at both ends or an air column in a pipe — the repeated reflections eventually produce a steady, non-moving wave pattern.
Beats
When two sound waves of nearly the same frequency travel through the same medium and are heard together, something remarkable happens. You do not hear two separate tones.
Summary
- A wave is a disturbance that propagates through a medium without transporting matter; it transfers energy and momentum.
Points to Ponder
1. A wave is not the bulk movement of the medium itself. Wind, for example, involves air molecules physically travelling from one location to another.
Exercises
+−Show 19 questionsHide questions19 questions
- 14.1A string of mass $2.50\ \text{kg}$ is under a tension of $200\ \text{N}$. The length of the stretched string is $20.0\ \text{m}$. If the tra…Free
- 14.2A stone dropped from the top of a tower of height $300\ \text{m}$ splashes into the water of a pond near the base of the tower. When is the…Free
- 14.3A steel wire has a length of $12.0\ \text{m}$ and a mass of $2.10\ \text{kg}$. What should be the tension in the wire so that speed of a tra…Free
- 14.4Use the formula $v = \sqrt{\dfrac{\gamma P}{\rho}}$ to explain why the speed of sound in air (a) is independent of pressure, (b) increases w…Preview
- 14.5You have learnt that a travelling wave in one dimension is represented by a function $y = f(x, t)$ where $x$ and $t$ must appear in the comb…Preview
- 14.6A bat emits ultrasonic sound of frequency $1000\ \text{kHz}$ in air. If the sound meets a water surface, what is the wavelength of (a) the r…Preview
- 14.7A hospital uses an ultrasonic scanner to locate tumours in a tissue. What is the wavelength of sound in the tissue in which the speed of sou…Preview
- 14.8A transverse harmonic wave on a string is described by $$y(x, t) = 3.0 \sin(36\,t + 0.018\,x + \pi/4)$$ where $x$ and $y$ are in cm and $t$…Preview
- 14.9For the wave described in Exercise 14.8, plot the displacement ($y$) versus ($t$) graphs for $x = 0$, $2$ and $4\ \text{cm}$. What are the s…Preview
- 14.10For the travelling harmonic wave $$y(x, t) = 2.0 \cos 2\pi(10t - 0.0080\,x + 0.35)$$ where $x$ and $y$ are in cm and $t$ in s. Calculate the…Preview
- 14.11The transverse displacement of a string (clamped at its both ends) is given by $$y(x, t) = 0.06 \sin\left(\frac{2\pi}{3}\,x\right) \cos(120\…Preview
- 14.12(i) For the wave on a string described in Exercise 14.11, do all the points on the string oscillate with the same (a) frequency, (b) phase,…Preview
- 14.13Given below are some functions of $x$ and $t$ to represent the displacement (transverse or longitudinal) of an elastic wave. State which of…Preview
- 14.14A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of $45\ \text{Hz}$. The mass of the wire is $3…Preview
- 14.15A metre-long tube open at one end, with a movable piston at the other end, shows resonance with a fixed frequency source (a tuning fork of f…Preview
- 14.16A steel rod $100\ \text{cm}$ long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod are given to be…Preview
- 14.17A pipe $20\ \text{cm}$ long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a $430\ \text{Hz}$ source? Will t…Preview
- 14.18Two sitar strings $A$ and $B$ playing the note 'Ga' are slightly out of tune and produce beats of frequency $6\ \text{Hz}$. The tension in t…Preview
- 14.19Explain why (or how): (a) in a sound wave, a displacement node is a pressure antinode and vice versa, (b) bats can ascertain distances, dire…Preview
Exemplar Problems
Higher-order thinking / exemplar-style practice problems.
+−Show 33 questionsHide questions33 questions
- Q1Water waves produced by a motor boat sailing in water are (a) neither longitudinal nor transverse. (b) both longitudinal and transverse. (c)…Free
- Q2Sound waves of wavelength $\lambda$ travelling in a medium with a speed of $v$ m/s enter into another medium where its speed is $2v$ m/s. Wa…Free
- Q3Speed of sound wave in air (a) is independent of temperature. (b) increases with pressure. (c) increases with increase in humidity. (d) decr…Free
- Q4Change in temperature of the medium changes (a) frequency of sound waves. (b) amplitude of sound waves. (c) wavelength of sound waves. (d) l…Preview
- Q5With propagation of longitudinal waves through a medium, the quantity transmitted is (a) matter. (b) energy. (c) energy and matter. (d) ener…Preview
- Q6Which of the following statements are true for wave motion? (a) Mechanical transverse waves can propagate through all mediums. (b) Longitudi…Preview
- Q7A sound wave is passing through air column in the form of compression and rarefaction. In consecutive compressions and rarefactions, (a) den…Preview
- Q8Equation of a plane progressive wave is given by $y = 0.6\sin 2\pi\left(t - \dfrac{x}{2}\right)$. On reflection from a denser medium its amp…Preview
- Q9A string of mass 2.5 kg is under a tension of 200 N. The length of the stretched string is 20.0 m. If the transverse jerk is struck at one e…Preview
- Q10A transverse harmonic wave on a string is described by $y(x,t) = 3.0\sin(36t + 0.018x + \pi/4)$ where $x$ and $y$ are in cm and $t$ is in s.…Preview
- Q11The displacement of a string is given by $y(x,t) = 0.06\sin(2\pi x/3)\cos(120\pi t)$ where $x$ and $y$ are in m and $t$ in s. The length of…Preview
- Q12Speed of sound waves in a fluid depends upon (Note: more than one of the given options may be correct.) (a) directty on density of the mediu…Preview
- Q13During propagation of a plane progressive mechanical wave (Note: more than one of the given options may be correct.) (a) all the particles a…Preview
- Q14The transverse displacement of a string (clamped at its both ends) is given by $y(x,t) = 0.06\sin(2\pi x/3)\cos(120\pi t)$. All the points o…Preview
- Q15Which of the following statements are true for a stationary wave? (Note: more than one of the given options may be correct.) (a) Every parti…Preview
- Q16A sonometer wire is vibrating in resonance with a tuning fork. Keeping the tension applied same, the length of the wire is doubled. Under wh…Preview
- Q17An organ pipe of length $L$ open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of 480 Hz. What shou…Preview
- Q18A tuning fork A, marked 512 Hz, produces 5 beats per second, where sounded with another unmarked tuning fork B. If B is loaded with wax the…Preview
- Q19The displacement of an elastic wave is given by the function $y = 3\sin\omega t + 4\cos\omega t$. where $y$ is in cm and $t$ is in second. C…Preview
- Q20A sitar wire is replaced by another wire of same length and material but of three times the earlier radius. If the tension in the wire remai…Preview
- Q21At what temperatures (in $^{\circ}$C) will the speed of sound in air be 3 times its value at $0^{\circ}$C?Preview
- Q22When two waves of almost equal frequencies $n_1$ and $n_2$ reach at a point simultaneously, what is the time interval between successive max…Preview
- Q23A steel wire has a length of 12 m and a mass of 2.10 kg. What will be the speed of a transverse wave on this wire when a tension of $2.06 \t…Preview
- Q24A pipe 20 cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a source of 1237.5 Hz ?(sound velocity in a…Preview
- Q25The shape of a stretched string is recorded at five successive instants during one full period $T$: at $t=0$ the string is a sinusoidal curv…Preview
- Q26A stationary wave on a stretched string is recorded at two instants of time. At the first instant ($t=0$) the string is sinusoidal: with the…Preview
- Q27A tuning fork vibrating at 512 Hz is held just above the open upper end of a long vertical glass tube. The lower end of the tube is joined b…Preview
- Q28Show that when a string fixed at its two ends vibrates in 1 loop, 2 loops, 3 loops and 4 loops, the frequencies are in the ratio 1:2:3:4.Preview
- Q29The earth has a radius of 6400 km. The inner core of 1000 km radius is solid. Outside it, there is a region from 1000 km to a radius of 3500…Preview
- Q30If $c$ is r.m.s. speed of molecules in a gas and $v$ is the speed of sound waves in the gas, show that $c/v$ is constant and independent of…Preview
- Q31Given below are some functions of $x$ and $t$ to represent the displacement of an elastic wave. (a) $y = 5\cos(4x)\sin(20t)$ (b) $y = 4\sin(…Preview
- Q32In the given progressive wave $y = 5\sin(100\pi t - 0.4\pi x)$ where $y$ and $x$ are in m, $t$ is in s. What is the (a) amplitude (b) wave l…Preview
- Q33For the harmonic travelling wave $y = 2\cos 2\pi(10t - 0.0080x + 3.5)$ where $x$ and $y$ are in cm and $t$ is second. What is the phase diff…Preview