1. Physics

2. Session
Wave and Sound - 3

3. Session Objectives

4. Session Objective Periodic Sound Waves
Intensity of Sound waves - Sound Level
Standing Waves (Wave Function)
Position of Nodes & antinodes in standing waves

5. Periodic Sound Waves The general form of the wave function is
In a periodic wave, the displacement repeats itself after a fixed periodic length , i.e.
where n = Integer

6. Intensity of Sound waves - Sound Level
where v = Velocity of the wave in that medium
= Frequency of particle oscillation
A = Amplitude

7. Intensity of Sound waves - Sound Level
Also the intensity level L of a sound of intensity ‘I’ is represented as
where I0 = Zero level of intensity or threshold intensity
Intensity level is generally expressed in ‘decibels’.

8. Standing Waves (Wave Function)
Two equal sine waves travel along a stretched string(length l) from opposite directions.

9. Position of Nodes in standing waves
For nodes, amplitude of the particles is zero.
where n is an integer.

10. Position of Antinodes in standing waves
For antinodes, amplitude of the particles is maximum.

11. Class Test

12. Class Exercise - 1
A sine wave is traveling in a medium. A particular particle has zero displacement at a certain instant. The particle closest to it having zero displacement is at a distance of

13. Solution
Particles which are at distance from each other, have same displacement.
Hence answer is (c).

14. Class Exercise - 2
A sonometer wire of length vibrates in fundamental mode when excited by a tuning fork of frequency 416 Hz. If the length is doubled, keeping other things same, the string will vibrate with a frequency of
(a) 416 Hz (b) 208 Hz
(c) 832 Hz (d) Stop vibrating
Solution :-
Hence answer is (a).

15. Class Exercise - 3
A standing wave is produced on a string clamped at one end and free at the other. The length of the string must be an integral multiple of
Solution :-
This is condition for standing waves.
Hence answer is (d).

16. Class Exercise - 4
Two strings A and B, made of same material, are stretched by same tension. The radius of string A is double the radius of B. The transverse wave travels on A with speed VA and on B with speed
VB. The ratio is
(a) (b) 2
(c) (d) 4

17. Solution
Hence answer is (a).

18. Class Exercise - 5
The amplitude of sound is doubled and the frequency is reduced to one-fourth. The intensity of sound at the same point will be
(a) increased by a factor of 2 (b) increased by a factor of 4 (c) decreased by a factor of 2 (d) decreased by a factor of 4

19. Solution
Hence answer is (d).

20. Class Exercise - 6
A standing wave having three nodes and two antinodes is formed between two atoms having a distance of 1.21 Å between them. The wavelength of the standing wave is
(a) 1.21 Å (b) 2.42 Å
(c) 6.05 Å (d) 3.63 Å

21. Solution
In this case
Hence answer is (a).

22. Class Exercise - 7
In a sinusoidal wave, the time required for a particular point to move from the maximum displacement to zero displacement is s. The frequency of the wave is
(a) 1.47 Hz (b) 0.36 Hz
(c) 0.73 Hz (d) 2.94 Hz

23. Solution
T = 4 × = 0.68 s
Hence answer is (a).

24. Class Exercise - 8
Particle displacements (in centimeters) in a standing wave are given by The distance between a node and the next antinode's is
(a) 2.5 cm (b) 5 cm
(c) 7.5 cm (d) 10 cm

25. Solution Distance between a node and an antinode is .
Hence answer is (b).

26. Class Exercise - 9
Transverse waves of same frequency are generated in two steel wires A and B. The diameter of A is twice that of B and tension in A is half that in B. The ratio of velocities of waves in A and B is
(a) 1 : 2 (b)
(c) (d)

27. Solution
Putting the values, we get
Hence answer is (c).

28. Class Exercise - 10
A wave represented by is superimposed with another wave to form a standing wave, such that point x = 0 is a node. Equation of the other wave is
(a) (b)
(c) (d)

29. Solution
For formation of stationary waves two waves should travel in opposite directions. Hence, the waves are (a) and (c) but (a) is not fulfilling the given condition completely.
Hence answer is (b).

30. Thank you