CBSE Class 11 Physics Wave Motion Basic Problems

1. The following equation gives the displacement y at time t for a particle at a distance x. y = 0.01 sin 500 π(t–x/30) where all are in S.I. unit. Find
(a) the wavelength,
(b) the speed of the wave
(c) the velocity amplitude of the particles of the medium.
(d) the acceleration amplitude of the particles of the medium.

2. A stationary wave is given by y = 5 sin πx/3  cos 40 πt where x and y are in cm and t is in seconds.
(a) What are the amplitude and velocity of the component waves whose superposition can give rise to this vibration?
(b) What is the distance between the nodes?
(c) What is the velocity of a particle of the string at the position x = 1.5 cm when t = 9/8 s?

3. The loudest painless sound produces a pressure amplitude of 28 Nm^–2. Calculate the intensity of this sound wave at STP. Density of air at STP = 1.3 kg m^–3 and speed of sound at STP = 332 m s^–1.

4. A stationary observer receives sound waves from two tuning forks, one of which approaches and the other recedes with the same velocity. As this takes place, the observer hears beats of frequency 2 Hz. Find the velocity of each tuning fork if their oscillation frequency v0 = 680 Hz and the velocity of sound in air is vs = 340 ms^–1.

5. A string of length 25 cm and mass 2.5 g is under tension. A pipe closed at one end is 40 cm long. When the string is set vibrating in its first overtone and the air in the pipe in its fundamental frequency, 8 beats per second are heard. It is observed that decreasing the tension in the string decreases the beat frequency. If the speed of sound in air 320 ms^–1, find the tension in the string.

6. A copper wire is held at the two ends by rigid supports. At 30°C the wire is just taut, with negligible tension. Find the speed of transverse waves along the wire at 10°C. Density of copper = 9 × 10³ kgm^–3, Young’s modulus = 1.1 × 10¹¹ Nm^–2 and coefficient of linear expansion = 1.7 × 10^–5 °C^–1.

7. A tube closed at one end has a vibrating diaphragm at the other end, which may be assumed to be a displacement node. It is found that when the frequency of the diaphragm is 200 Hz, a stationary wave pattern is set up in which the distance between adjacent nodes is 8 cm. When the frequency is gradually reduced, the stationary wave pattern disappears but another stationary wave pattern reappears at a frequency of 1600 Hz. Calculate.
(a) the speed of sound in air,
(b) the distance between adjacent nodes at a frequency of 1600 Hz.,
(c) the distance between the diaphragm and the closed end,
(d) the next lower frequencies at which stationary wave patterns will be obtained.

8. A travelling wave is produced on a long horizontal string by vibrating an end up and down sinusoidally. The amplitude of vibrating is 1.0 cm and the displacement becomes zero 200 times per second. The linear mass density of the string is 0.10 kg/m and it is kept under a tension of 90 N.
(a) Find the speed and the wavelength of the wave.
(b) Assume that the wave moves in the positive x-direction and at t = 0, the end x = 0 is at its positive extreme position. Write the wave equation.
(c) Find the velocity and acceleration of the particle at x = 50 cm at time t = 10 ms

9. The equation of a standing wave, produced on a string fixed at both ends, is y = (0.4 cm) sin[(0.314 cm^–1)x] cos [(600π s^–1)t]. What could be the smallest length of the string?

10. Figure shows an aluminium wire of length 60 cm joined to a steel wire of length 80 cm and stretched between two fixed supports. The tension produced is 40 N. The cross-sectional area of the steel wire is 1.0 mm and that of the aluminium wire is 3.0 mm². What could be the minimum frequency of a tuning fork which can produce standing waves in the system with the joint as a node? The density of aluminium is 2.6 g/cm³ and that of steel is 7.8 g/cm³.

11. A small source of sound S of frequency 500 Hz is attached to the end of a light string and is whirled in a vertical circle of radius 1.6 m. The string just remains tight where the source is at the highest point.

(a) An observer is located in the same vertical plane at a large distance and at the same height as the centre of the circle. The speed of sound in air = 330 m/s and g = 10 m/s². Find the maximum frequency heard by the observer.