Waves Class 11 Notes CBSE Physics Chapter 15 (Free PDF Download)

Section – A (1 Mark Questions)

1. Why can the transverse waves not be produced in air?

Ans. For air, the modulus of rigidity is zero or it does not possess property of possession. Therefore, transverse Waves cannot be produced.

2.  Why are all stringed instruments provided with hollow boxes?

Ans. The stringed instruments are provided with a hollow box called sound box. When the strings are set into vibration, forced vibrations are produced in the sound box. Since sound box has a large area, it sets a large volume of air into vibration. This produces a loud sound of the same frequency of that of the string.

3.  Can beats be produced in two light sources of nearly equal frequencies?

Ans. No, because the emission of light is a random and rapid phenomenon and instead of beats, we get uniform intensity.

4. A stationary boat is rocked by waves whose crests are 100m apart velocity is 25m/s. Find the time after which the boat bounces up every time.

Ans. $v=n\lambda$

$v=\dfrac{\lambda }{T}\Rightarrow T=\dfrac{\lambda }{v}$

$v=\dfrac{100}{25}=4s$

5. A long string having mass density as 0.01kg/m is subjected to a tension of 64N. Then find the speed of the transverse wave on the string.

Ans. $v=\sqrt{\dfrac{T}{\mu }}=\sqrt{\dfrac{60}{0\cdot 01}}$

$v=\sqrt{6400}=80m/s$

Section – B (2 Marks Questions)

6. Three harmonic waves of same frequency (f) and intensity $I_{0}$ having initial phase angles $0,\dfrac{\pi }{4},\dfrac{\pi }{4}$ rad respectively. When they are superimposed, find the resultant intensity.

Ans. Amplitude can be added using vector addition

A_{resultant}=(\sqrt{2}+1)A

Since $1\varpropto A^{2}$ ,Where I is intensity 

Therefore, $I_{res}=\left ( \sqrt{2}+1 \right )^{2}I_{0}=5\cdot 8I_{0}(Approx)$

7. Guitar strings X and Y striking the note ‘Ga’ are a little out of tune and give beats at 6 Hz. When the string X is slightly loosened and the beat frequency becomes 3 Hz. Given that the original frequency of X is 324 Hz, find the frequency of Y.

Ans. Given,

Frequency of X, $f_{x}=324Hz$

Frequency of Y = fy

Beat’s frequency, n = 6 Hz

Also,

$n=\left | f_{x}\pm f_{y} \right |$

$6=324\pm f_{y}$

$\Rightarrow f_{y}=330\;Hz$ or $318\;Hz$

As frequency drops with a decrease in tension in the string, thus $f_{y}$ cannot be 330 Hz

$\Rightarrow f_{y}=318\;Hz$

8. A narrow sound pulse (for example, a short pip by a whistle) is sent across a medium.

(a) Does the pulse have a definite (i) frequency, (ii) wavelength, (iii) speed of propagation?

(b) If the pulse rate is 1 after every 20 s, (that is the whistle is blown for a split of second after every 20 s), is the frequency of the note produces by the whistle equal to 1/20 or 0.05 Hz?

Ans.

(a) The speed of propagation is definite; it is equal to the speed of the sound in air. The wavelength and frequency will not be definite.

(b) The frequency of the note produced by a whistle is not 1/20 = 0.05 Hz. However, 0.05 Hz is the frequency of repetition of the short pip of the whistle.

9. A transverse wave passes through a string with the equation y = 10 sin $\pi$ (0.02 x - 2.00t) where x is in meter and t in second. Then find the maximum velocity of the particle in wave motion.

Ans. $y=10sin\pi \left ( 0\cdot 02x-2\cdot 00t \right )$

In order to derive maximum velocity,

$\dfrac{dy}{dt}=-20\pi cos\pi \left ( 0\cdot 02x-2\cdot 00t \right )$

$v=-20\pi cos\pi \left ( 0\cdot 02x-2\cdot 00t \right )$

$v_{max}=20\pi$

$v_{max}=63ms^{-1}$

10. Two tuning forks P and Q when set vibrating, given 4 beats/s. If a prong of the fork P is filed, the beats are reduced to 2 beats/s. What is frequency of P, if that of Q is 250 Hz ?

Ans. If fork P is filed then frequency increases, increased frequency is given by

${P}'-Q=2$

${P}'-250=2$

${P}'=252Hz$

Therefore, initial frequency of P is lower than 252Hz and at that time 4 beats are heard

Q-P=4

250-P=4

P=246Hz

PDF Summary - Class 11 Physics  Oscillations Notes (Chapter 15)

The last point to be highlighted is the emphasis of an important misconception of waves. Waves transfer energy but do not transfer mass. To see this an easy way is to take an example of a floating ball a few yards out to sea. As the propagation i.e., travelling of waves towards the shore the ball which was in the example will not come towards the shore. 

Eventually, it may come to shore due to a few other factors like winds, tides, or current, but the waves themselves will not carry the ball with them. A mass only moved by the wave which is perpendicular to the direction of propagation and in this case up and down as illustrated in the figure which is given below:

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Depending on the direction of the oscillation of the wave, A wave can be transverse or longitudinal. When a disturbance is caused due to oscillations perpendicular to the propagation the transverse waves occur at the same time. When the oscillations are parallel to the direction of propagation then the waves which are longitudinal occur. While both longitudinal and transverse can be mechanical waves as all electromagnetic waves are transverse waves. An example of longitudinal waves is Sound.

Waveforms 

The famous scientist and physicist d'Alembert's formulated the formula of F or shape involves the argument that is denoted as x − vt. In this argument, we can say Constant values which correspond to constant values of F, and if x increases then the rate that vt increases here the constant of values occur. That can be said as the wave-shaped like the F function which will move in the positive direction of x at velocity v and G will propagate at the same speed in the negative direction of x.

In another case of a periodic function F with period denoted as λ, that is  F(x + λ − vt) = F(x − vt) in this the periodicity of F in space has a meaning that a snapshot of the wave which at a given time denoted as t finds the wave varying periodically in space with period λ is denoted as the wavelength of the wave. In a similar manner this periodicity of F implies a periodicity in time t as well that is F(x − v(t + T)) = F(x − vt) 

and then vT = λ, so we can observe the wave at a fixed location that is x that finds the wave undulating periodically in time with period T = λ/v.

Phase Velocity and Group Velocity

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If we consider a red square then the red square moves with the phase velocity, while the green circles which we take as another mark propagates with the group velocity.

There are two velocities that are associated with waves that are the group and the phase velocity.

Velocity which is of the same phase is defined as the rate at which the phase of the wave propagates that to in space at any phase which is given by the wave for example the crest that appears to travel at the phase velocity. The phase velocity is denoted as wavelength λ that is lambda and time period as T.

Group velocity that is the second part is the property of waves that have a defined envelope measuring propagation through space that is of phase velocity and of the overall shape of the waves' amplitude and envelope or modulation of the wave.

Types and Features of Waves

There are two kinds of Waves that are transverse and the longitudinal waves. Transverse waves are like those which are on the water, with the surface going down and up, and longitudinal waves are like those similar to sound waves. The transverse wave high point is called the crest whereas the low point is called the trough. For waves that are longitudinal, the refractions and compressions are analogous to the through and crests and transverse waves. 

The distance between successive troughs and crests or is called the wavelength. The height of a wave is defined as the amplitude. How many troughs and crests pass a specific point during a unit of time is known as the frequency. The wave velocity can be expressed as the wavelength which multiplied by the frequency.

Waves can travel far distances even though the oscillation at one point is small. For example, a thunderclap can be heard kilometers away from where it is actually present yet the sound carried manifests itself at any point only as a minute refraction of air and compressions.

Waves display several basic phenomena like In reflection phenomenon a wave encounters an obstacle and it is reflected back. In the phenomenon of refraction, a wave bends when it enters a medium through it has a different speed. In the phenomenon of diffraction, the waves bend when they pass around small obstacles and spread out when they go through small openings that are present.