1. Physics

2. Session
Wave and Sound - 1

3. Session Objectives

4. Session Objective Introduction to wave motion (Terminologies)
Types of waves
Sinusoidal waves
Characteristics of sine waves
Speed of mechanical waves in one-dimensional translatory motion
Velocity of transverse mechanical waves in strings
Phase and path difference

5. Introduction to wave motion (terminologies)
‘A wave is a disturbance which propagates energy (and momentum) from one place to another without the transport of matter.’
Amplitude:- Maximum displacement of the elements from their equilibrium position T
x, t A
Time period:- Time any wave takes to complete one oscillation.

6. Introduction to wave motion (terminologies)
Frequency :- It is defined as the number of oscillations per unit time.
Wavelength :- It is the distance (parallel to the direction of wave propagation) between the consecutive repetitions of the shape of the wave. It is the distance between two consecutive troughs or crests
Propagation constant :- The quantity is called the propagation constant,

7. Types of Waves
Mechanical waves: The waves which require medium for their propagation are called mechanical waves.e.g. sound waves
Non-mechanical waves: The waves which do not require medium for their propagation are called non-mechanical waves, e.g. light

8. Types of Waves
Transverse waves: If the particles of the medium vibrate at right angle to the direction of wave motion or energy propagation, the wave is called transverse wave e.g. waves on strings.

9. Types of Waves
Longitudinal waves: If the particles of a medium vibrate in the direction of wave motion, the wave is called longitudinal wave. e.g. sound waves

10. Sinusoidal waves
At any time t, the displacement y of the element located at a position x is given by y x
Sinusoidal wave

11. Characteristics of Sine Waves
The sinusoidal wave represented by above equation is periodic in position and time.
The equation of the wave traveling along positive x-axis is given by
and moving along negative x-axis is given by
In general, we can write

12. Characteristics of Sine Waves
This equation can be represented as

13. Speed of mechanical waves in one-dimensional translatory motion
The relation is valid for all types of progressive waves.

14. Velocity of Transverse mechanical waves on strings
F = 2T sinq
Now F = Dma

15. Phase and Path Difference
If the shape of the wave does not change as the wave propagates in a medium, with increase in t, x will also increase in such a way that x y

16. Class Test

17. Class Exercise - 1
The equation of a transverse wave is given by y = 10 sinp (0.01x – 2t) where x and y are in centimeters and t is in seconds, its frequency is
(a) 10 Hz (b) 2 Hz
(c) 1 Hz (d) 0.01 Hz

18. Solution Comparing with equation y = 10 sinp(0.01x – 2t) We get,
i.e. f = 1 Hz
Hence answer is (c).

19. Class Exercise - 2 A transverse wave is described by the
equation The
maximum particle velocity is equal to four times the wave velocity if

20. Solution We know that the maximum particle velocity
From the given equation, we get
Wave velocity v = fl
Given condition
Hence answer is (b).

21. Class Exercise - 3
A source of frequency 500 Hz emits waves of wavelength 0.2 m. How long does it take for the wave to travel 300 m?
(a) 70 s (b) 60 s
(c) 12 s (d) 3 s

22. Solution Using the relation we get, v = 500 × 0.2 v = 100 m/s
Hence answer is (d).

23. Class Exercise - 4 The equation of a plane wave is given
by where y is in
centimeters and t is in seconds. The phase difference at any instant between the points separated by 150 cm is

24. Solution
We know that,
l = 300 cm
Hence answer is (b).

25. Class Exercise - 5
A stone is dropped into a well. If the depth of water below the top be h and velocity of sound is v, the splash in water is heard after T second, then

26. Solution
Time taken by the stone to fall to the surface of water is given by
t2 — time taken by sound Total time T = t1 + t2
Hence answer is (a).

27. Class Exercise - 6
A man standing symmetrically between two cliffs claps his hands and starts hearing a series of echoes at intervals of 1 s. The speed of sound in air is 340 m/s, the distance between parallel cliffs must be
(a) 340 m (b) 680 m
(c) 1,020 m (d) 170 m

28. Solution Let the distance of each cliff from the man be x.
Distance between cliffs = 2x
= 2 × 170 = 340 m
Hence answer is (a).

29. Class Exercise - 7
The relation between the particle velocity and wave velocity in a wave is

30. Solution
Hence answer is (c).

31. Class Exercise - 8
A 5.5 m length of string has a mass of kg. If the tension in the string is 77 N, the speed of the wave on the string is
(a) 110 ms–1 (b) 164 ms–1
(c) 77 ms–1 (d) 102 ms–1

32. Solution
Mass per unit length =
v = 110 m/s
Hence answer is (a).

33. Class Exercise - 9
An observer standing at sea coast observes 54 waves reaching the coast per minute, if the wavelength of the wave is 10 m, its velocity is
(a) 3 m/s (b) 6 m/s
(c) 9 m/s (d) 12 m/s

34. Solution As 54 waves reach the coast per minute v = 9 m/s
Hence answer is (c).

35. Class Exercise - 10
A progressive wave of frequency 500 Hz is traveling with a velocity of 360 m/s. How far apart are the two points 60° out of phase?
(a) 0.12 m (b) 0.06 m
(c) 0.24 m (d) 0.36 m

36. Solution
Hence answer is (a).

37. Thank you