# Chapter 15 – Waves Questions and Answers: NCERT Solutions for Class 11 Physics

Class 11 Physics NCERT book solutions for Chapter 15 - Waves Questions and Answers.

Education Blogs Chapter 15 – Waves Questions and Answers: NCERT Solutions for Class 11...

Class 11 Physics NCERT book solutions for Chapter 15 - Waves Questions and Answers.

frequency υ= 4.2 MHz = 4.2 x 106Hz

.’. Wavelength, A = υ/V = 1700/(4.2 x 106) =4.1 x 10-4m.

y(x, t) = 3.0 sin (36 t + 0.018 x + π/4)

where x and y are in cm and t in s. The positive direction of x is from left to right.

(a) Is this a travelling wave or a stationary wave? If it is travelling, what are the speed and direction of its propagation ?

(b) What are its amplitude and frequency?

(c) What is the initial phase at the origin?

(d) What is the least distance between two successive crests in the wave?

Similar graphs are obtained for y x = 2 cm and x = 4 cm. The (incm) oscillatory motion in the travelling wave only differs in respect of phase. Amplitude and frequency of oscillatory motion remains the same in all the cases.

y(x, t) = 2.0 cos 2π (10t – 0.0080x + 0.35)

where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion oftwo points separated by a distance of

(a) 4 m (b) 0.5 m

(c) λ/2 (d) 3λ/4.

where x, y are in m and t in s. The length of the string is 1.5 m and its mass is 3 x 10-2kg. Answer the following:

(i) Does the function represent a travelling or a stationary wave?

(ii) Interpret the wave as a superimposition of two waves travelling in opposite directions. What are the wavelength, frequency and speed of propagation of each wave?

(iii) Determine the tension in the string.

y(x, t) = 0.06 sin 2π/3 x cos 120 πt …(1)

(i)As the equation involves harmonic functions of x and t separately, it represents a stationary wave.

(a) Yes, all the sring particles, except nodes, vibrate with the same frequency v = 60 Hz.

(b) As all string particles lie in one segment, all of them are in same phase.

(c) Amplitude varies from particle to particle. At antinode, amplitude = 2A = 0.06 m. It gradually falls on going towards nodes and at nodes, and at nodes, it is zero.

(ii) Amplitude at a point x = 0.375 m will be obtained by putting cos (120 πt) as + 1 in the wave equation.

(b) It does not represent either a travelling wave or a stationary wave.

(c) It is a representation for the travelling wave.

(d) It is a superposition of two stationary wave.

On simplification, n = 1

Now, (2n-1)υ/4l1= 340. Substituting values

(2 x 1 -1) υ x 100/4 x 25.5 = 340 or υ =346.8 ms-1

When the rod is clamped at the middle, then in the fundamental mode of vibration of the rod, a node is formed at the middle and ant mode is formed at each end.

Then, υ1= 324 Hz, υ2= ?

Number of beats, b = 6

υ2= υ1± b = 324 ± 6 !.e., υ2= 330 Hz or 318 Hz

Since the frequency is directly proportional to square root of tension, on decreasing the tension in the string A, its frequency υ1will be reduced i.e., number of beats will increase if υ2= 330 Hz. This is not so because number of beats become 3.

Therefore, it is concluded that the frequency υ2= 318 Hz. because on reducing the tension in the string A, its frequency may be reduced to 321 Hz, thereby giving 3 beats with υ2= 318 Hz.

(a) in a sound wave, a displacement node is a pressure antinode and vice versa.

(b) bats can ascertain distances, directions, nature and sizes of the obstacles without any “eyes”.

(c) a violin note and sitar note may have the same frequency, yet we can distinguish between the two notes.

(d) solids can support both longitudinal and transverse waves, but only longitudinal waves can propagate in gases, and

(e) the shape of a pulse gets distorted during propagation in a dispersive medium.

(b) Bats emit ultrasonic waves of high frequency from their mouths. These waves after being reflected back from the obstacles on their path are observed by the bats. These waves give them an idea of distance, direction, nature and size of the obstacles.

(c) The quality of a violin note is different from the quality of sitar. Therefore, they emit different harmonics which can be observed by human ear and used to differentiate between the two notes.

(d) This is due to the fact that gases have only the bulk modulus of elasticity whereas solids have both, the shear modulus as well as the bulk modulus of elasticity.

(e) A pulse of sound consists of a combination of waves of different wavelength. In a dispersive medium, these waves travel with different velocities giving rise to the distortion in the wave.

(i) (a) When the train approaches the platform (i.e., the observer at rest),

(a) what are the displacement and velocity of oscillation of a point at x = 1 cm, and t = 1s? Is this velocity equal to the velocity of wave propagation?

(b) Locate the points of the string which have the same transverse displacement and velocity as the x = 1 cm point at t = 2s, 5s and 11s.

Let distance of earthquake centre = sKm

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