Physics

Session Wave and Sound - 1

Session Objectives

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

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.

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,

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

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.

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

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

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

Characteristics of Sine Waves This equation can be represented as

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

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

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

Class Test

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

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

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

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

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

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

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

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

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

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).

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

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

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

Solution Hence answer is (c).

Class Exercise - 8 A 5.5 m length of string has a mass of 0.035 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

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

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

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

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

Solution Hence answer is (a).

Thank you