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# Physics - PowerPoint PPT Presentation

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

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Presentation Transcript
Session

Wave and Sound - 1

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

T

A

x, t

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

Time period:- Time any wave takes to complete one oscillation.

Propagation constant :- The quantity is called the propagation constant,

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

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

y

x

Sinusoidal waves

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

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

The relation is valid for all types of progressive waves.

y

x

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

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

We get,

i.e. f = 1 Hz

Solution

Comparing with equation

y = 10 sinp(0.01x – 2t)

A transverse wave is described by the

equation . The

maximum particle velocity is equal to four times the wave velocity if

Class Exercise - 2

Given condition

Solution

We know that the maximum particlevelocity

From the given equation, we get

Wave velocity v = fl

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

Class Exercise - 3

Using the relation

Solution

we get, v = 500 × 0.2

v = 100 m/s

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

Class Exercise - 4
Solution

We know that,

l = 300 cm

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

Class Exercise - 5
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

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

Solution

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

Mass per unit length =

Solution

v = 110 m/s

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