Acoustics: Introduction to Sound, Waves, Echo, and Doppler Effect | 10th Science Chapter 5

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Acoustics - Introduction

INTRODUCTION

Sound plays a major role in our lives. We communicate with each other mainly through sound. In our daily life, we hear a variety of sounds produced by different sources like humans, animals, vehicle horns, etc. Hence, it becomes inevitable to understand how sound is produced, how it is propagated and how you hear the sound from various sources. It is sometimes misinterpreted that acoustics only deals with musical instruments and design of auditoria and concert halls. But, acoustics is a branch of physics that deals with production, transmission, reception, control, and effects of sound. You have studied about propagation and properties of sound waves in IX standard. In this lesson we will study about reflection of sound waves, Echo and Doppler effect.

Introduction to Newton's Laws of Motion | 10th Science Chapter 1

Newton’s Laws of Motion

NEWTON’S LAWS OF MOTION

This law states that every body continues to be in its state of rest or the state of uniform motion along a straight line unless it is acted upon by some external force. It gives the definition of force as well as inertia.

2. Force

Force is an external effort in the form of push or pull, which:

1. produces or tries to produce the motion of a static body.
2. stops or tries to stop a moving body.
3. changes or tries to change the direction of motion of a moving body.

Force has both magnitude and direction.

So, it is a vector quantity.

3. Types of forces

Based on the direction in which the forces act, they can be classified into two types as:

(a) Like parallel forces and (b) Unlike parallel forces.

a) Like parallel forces: Two or more forces of equal or unequal magnitude acting along the same direction, parallel to each other are called like parallel forces.

b) Unlike parallel forces: If two or more equal forces or unequal forces act along opposite directions parallel to each other, then they are called unlike parallel forces. Action of forces are given in Table 1.1.

4. Resultant Force

When several forces act simultaneously on the same body, then the combined effect of the multiple forces can be represented by a single force, which is termed as ‘resultant force’. It is equal to the vector sum (adding the magnitude of the forces with their direction) of all the forces.

If the resultant force of all the forces acting on a body is equal to zero, then the body will be in equilibrium. Such forces are called balanced forces. If the resultant force is not equal to zero, then it causes the motion of the body due to unbalanced forces.

Examples: Drawing water from a well, force applied with a crow bar, forces on a weight balance, etc.

A system can be brought to equilibrium by applying another force, which is equal to the resultant force in magnitude, but opposite in direction. Such force is called as ‘Equilibrant’.

5. Rotating Effect of Force

Have you observed the position of the handle in a door? It is always placed at the edge of door and not at some other place. Why? Have you tried to push a door by placing your hand closer to the hinges or the fixed edge? What do you observe?

The door can be easily opened or closed when you apply the force at a point far away from the fixed edge. In this case, the effect of the force you apply is to turn the door about the fixed edge. This turning effect of the applied force is more when the distance between the fixed edge and the point of application of force is more.

The axis of the fixed edge about which the door is rotated is called as the ‘axis of rotation’. Fix one end of a rod to the floor/wall, and apply a force at the other end tangentially.

The rod will be turned about the fixed point is called as ‘point of rotation’.

6. Moment of the Force

The rotating or turning effect of a force about a fixed point or fixed axis is called moment of the force about that point or torque (τ). It is measured by the product of the force (F) and the perpendicular distance (d) between the fixed point or the fixed axis and the line of action of the force. τ = F × d

Torque is a vector quantity. It is acting along the direction, perpendicular to the plane containing the line of action of force and the distance. Its SI unit is N m.

Couple: Two equal and unlike parallel forces applied simultaneously at two distinct points constitute a couple. The line of action of the two forces does not coincide. It does not produce any translatory motion since the resultant is zero. But, a couple results in causes the rotation of the body. Rotating effect of a couple is known as moment of a couple.

Examples: Turning a tap, winding or unwinding a screw, spinning of a top, etc.

Moment of a couple is measured by the product of any one of the forces and the perpendicular distance between the line of action of two forces. The turning effect of a couple is measured by the magnitude of its moment.

Moment of a couple = Force × perpendicular distance between the line of action of forces

M = F × S

The unit of moment of a couple is newton metre (N m) in SI system and dyne cm in CGS system.

By convention, the direction of moment of a force or couple is taken as positive if the body is rotated in the anti-clockwise direction and negative if it is rotated in the clockwise direction.

They are shown in Figures 1.4 (a and b)

7. Application of Torque

1. Gears:

A gear is a circular wheel with teeth around its rim. It helps to change the speed of rotation of a wheel by changing the torque and helps to transmit power.

2. Seasaw

Most of you have played on the seasaw. Since there is a difference in the weight of the persons sitting on it, the heavier person lifts the lighter person. When the heavier person comes closer to the pivot point (fulcrum) the distance of the line of action of the force decreases. It causes less amount of torque to act on it. This enables the lighter person to lift the heavier person.

3. Steering Wheel

A small steering wheel enables you to manoeuore a car easily by transferring a torque to the wheels with less effort.

8. Principle of Moments

When a number of like or unlike parallel forces act on a rigid body and the body is in equilibrium, then the algebraic sum of the moments in the clockwise direction is equal to the algebraic sum of the moments in the anticlockwise direction. In other words, at equilibrium, the algebraic sum of the moments of all the individual forces about any point is equal to zero.

In the illustration given in figure 1.5, the force F₁ produces an anticlockwise rotation at a distance d₁ from the point of pivot P (called fulcrum) and the force F₂ produces a clockwise rotation at a distance d₂ from the point of pivot P. The principle of moments can be written as follows:

Moment in clockwise direction = Moment in anticlockwise direction

F₁ × d₁ = F₂ × d₂

NEWTON’S SECOND LAW OF MOTION

According to this law, “the force acting on a body is directly proportional to the rate of change of linear momentum of the body and the change in momentum takes place in the direction of the force”.

This law helps us to measure the amount of force. So, it is also called as ‘law of force’. Let, ‘m’ be the mass of a moving body, moving along a straight line with an initial speed ‘u’ After a time interval of ‘t’, the velocity of the body changes to ‘v’ due to the impact of an unbalanced external force F.

Initial momentum of the body P_i = mu

Final momentum of the body P_f = mv

Change in momentum Δp = P_f – P_i

= mv – mu

By Newton’s second law of motion,

Force, F ∝ rate of change of momentum

F ∝ change in momentum / time

Here, k is the proportionality constant. k = 1 in all systems of units. Hence,

Since, acceleration = change in velocity/ time, a=(v-u)/t. Hence, we have

F = m × a

Force = mass × acceleration

No external force is required to maintain the motion of a body moving with uniform velocity. When the net force acting on a body is not equal to zero, then definitely the velocity of the body will change. Thus, change in momentum takes place in the direction of the force. The change may take place either in magnitude or in direction or in both.

Force is required to produce the acceleration of a body. In a uniform circular motion, even though the speed (magnitude of velocity) remains constant, the direction of the velocity changes at every point on the circular path. So, the acceleration is produced along the radius called as centripetal acceleration. The force, which produces this acceleration is called as centripetal force, about which you have learnt in class IX.

Units of force: SI unit of force is newton (N) and in C.G.S system its unit is dyne.

Definition of 1 newton (N): The amount of force required for a body of mass 1 kg produces an acceleration of 1 m s^–2, 1 N = 1 kg m s^–2

Definition of 1 dyne: The amount of force required for a body of mass 1 gram produces an acceleration of 1 cm s^–2, 1 dyne = 1 g cm s^–2; also 1 N = 10⁵ dyne.

Unit force:

The amount of force required to produce an acceleration of 1 m s^–2 in a body of mass kg is called ‘unit force’.

Gravitational unit of force:

In the SI system of units, gravitational unit of force is kilogram force, represented by kg f. In the CGS system its unit is gram force, represented by g f.

1 kg f = 1 kg × 9.8 m s^-2 = 9.8 N;

1 g f = 1 g × 980 cm s^-2 = 980 dyne

Introduction to Laws of Motion: Force and Motion Concepts | 10th Science Chapter 1

10th Science | Chapter 1: Laws of Motion

Introduction: Force and Motion

FORCE AND MOTION

According to Aristotle a Greek Philosopher and Scientist, the natural state of earthly bodies is ‘rest’. He stated that a moving body naturally comes to rest without any external influence of the force. Such motions are termed as ‘natural motion’ (Force independent). He also proposed that a force (a push or a pull) is needed to make the bodies to move from their natural state (rest) and behave contrary to their own natural state called as ‘violent motion’ (Force dependent). Further, he said, when two differnt mass bodies are dropped from a height, the heavier body falls faster than the lighter one.

Galileo proposed the following concepts about force, motion and inertia of bodies:

1. The natural state of all earthly bodies is either the state of rest or the state of uniform motion.
2. A body in motion will continue to be in the same state of motion as long as no external force is applied.
3. When a force is applied on bodies, they resist any change in their state. This property of bodies is called ‘inertia’.
4. When dropped from a height in vacuum, bodies of different size, shape and mass fall at the same rate and reach the ground at the same time.

SETS IX MATHS I, INTRODUCTION, MAHARASHTRA STANDARD 9. Video Explanation + Notes

In day-to-day life, we generally talk about a group or a collection of objects. e.g. a pack of cards, a group of students, a group of friends, etc.

1. The well-defined collection of objects is called a set.
2. Capital English letters A, B, C, etc. are used to denote a set.
3. The individual object of the set is known as the member or an element of the set.
4. The elements of the set are denoted by lower case letters a, b, c, etc.
5. If a is an element of set A, then it is written as a ∈ A, and is read as 'a is an element of set A' or 'a is a member of set A' or 'a belongs to set A'.
6. If a is not an element of set A, then it is written as a ∉ A. The symbol ∉ stands for 'is not an element of' or 'is not a member of'. Thus, it is read as 'a is not an element of set A' or 'a is not a member of set A' or 'a does not belong to set A'.

Let us see the set of numbers:

• (a) A set of natural numbers. N = {1, 2, 3, ...}
• (b) A set of whole numbers. W = {0, 1, 2, .....}
• (c) A set of integers. I = {... -3, -2, -1, 0, 1, 2, 3, ....}
• (d) Q is the set of rational numbers.
• (e) R is a set of real numbers.