List of top Questions asked in CBSE Class XI

1. at one of its extreme positions, 
2. at its mean position.

A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is 3.5 × 10^–2 kg and its linear mass density is 4.0 × 10^–2 kg m^–1. What is (a) the speed of a transverse wave on the string, and (b) the tension in the string?

Given below are some functions of x and t to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent (i) a travelling wave, (ii) a stationary wave or (iii) none at all: 

(a) y = 2 cos (3x) sin (10t) 

(b) \(y=2\sqrt{x-vt}\)

(c) y = 3 sin (5x – 0.5t) + 4 cos (5x – 0.5t) 

(d) y = cos x sin t + cos 2x sin 2t

The transverse displacement of a string (clamped at its both ends) is given by 

y(x, t) = 0.06 sin \((\frac{2π}{3 }x)\) cos (120 πt) 

where x and y are in m and t in s. The length of the string is 1.5 m and its mass is 3.0 ×10^–2 kg. 

Answer the following : 

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

(b) Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength, frequency, and speed of each wave?

(c) Determine the tension in the string

For the travelling harmonic wave 

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

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

(a) 4 m, 

(b) 0.5 m, 

(c) \(\frac{λ}{2}\), 

(d) \(\frac{3λ}{4}\)

A transverse harmonic wave on a string is described by

 y(x, t) = 3.0 sin (36 t + 0.018 x + \(\frac{π}{4}\)) 

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 ?

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 combination x – v t or x + v t, i.e. y = f (x ± v t). Is the converse true? Examine if the following functions for y can possibly represent a travelling wave : 

(a) (x – vt )² 

(b) log \([\frac{x + vt}{x_0} ] \)

(c) \(\frac{1}{(x + vt)}\)

Use the formula \(v=\sqrt\frac{γp}{ρ}\)  to explain why the speed of sound in air 

(a) is independent of pressure, 

(b) increases with temperature, 

(c) increases with humidity.

1. just after it is dropped from the window of a stationary train,
2. just after it is dropped from the window of a train running at a constant velocity of 36 \(\text {km}/\text h\),
3. just after it is dropped from the window of a train accelerating with 1 \(\text m \; \text s^{-2}\),
4. lying on the floor of a train which is accelerating with 1 \(\text m \; \text s^{-2}\), the stone being at rest relative to the train.

Neglect air resistance throughout.

1. during its upward motion,
2. during its downward motion,
3. at the highest point where it is momentarily at rest. Do your answers change if the pebble was thrown at an angle of 45° with the horizontal direction?

Ignore air resistance.

1. a drop of rain falling down with a constant speed,
2. a cork of mass 10 \(\text g\) floating on water,
3. a kite skillfully held stationary in the sky,
4. a car moving with a constant velocity of 30 \(\text {km} /\text h\) on a rough road,
5. a high-speed electron in space far from all material objects, and free of electric and magnetic fields.