•Law of length

First law tells that when the tension and the linear density are

constant, the frequency of the vibration is inversely proportional

to the length. For a given wire tension (T) and linear density

(m) are constant, the fundamental frequency of vibration (n) is

inversely proportional to the vibrating length (l),

i.e. n ∞ 1/l

or, nl = constant.

The fundamental frequency of vibration of a string (fixed at both

ends) is inversely proportional to the length of the string

provided its tension and its mass per unit length remain the

same.

•Law of tension

The second law states that, if the length and linear

density are constant, the frequency is directly

proportional to the square root of the tension. For the

length (l) and linear density (m) are constant, the

fundamental frequency (n) is directly proportional to the

square root of the tension (T),

i.e. n ∞ √T

or, n / √T = constant.

The fundamental frequency of a string is proportional to

the square root of its tension provided its length and

the mass per unit length remain the same.

iii) Law of mass

The third law is that, when the length and tension are constant, the

frequency is inversely proportional to the square root of linear density.

The fundamental frequency of a string is inversely proportional to the

square root of the linear mass density, i.e., mass per unit length

provided the length and the tension remain the same.

(iii) For the length (l) and tension (T) are constant, the fundamental

frequency (n) varies inversely as the square root of the linear density

(m),

i.e. n ∞ 1/√m

or, n√m = constant.

The laws of transverse vibration of the stretched string are verified by

using sonometer

A string undergoing transverse vibration illustrates the

vibrations of a guitar string or the standing wave nodes in a

studio monitoring room.

In this experiment the change in frequency produced when

the tension is increased in the string – will be measured.

From this the mass per unit length of the string / wire can be

derived.

This is called as the principle of the Melde's Experiment

APPARATUS- • Electrically maintained tuning fork Electrically maintained tuning fork • A stand with clamp and pulley A stand with clamp and pulley • A light weight pan A light weight pan • A weight box A weight box • Balance Balance • A battery with eliminator and connecting wires

THEORYA string can be set into vibrations by means of an electrically maintained tuning fork, maintained tuning fork, thereby producing stationary waves thereby producing stationary waves thereby producing stationary waves due to reflection of waves at the pulley.The end of the pulley where it touches the pulley and the position where it is fixed to theprong of tuning fork. prong of tuning fork. prong of tuning fork. ((i)For the transverse arrangement,the frequency is given by the frequency is given by the frequency is given by where ‘L’ is the length of thread in fundamental modes of vibrations, ‘T ’is the tension applied to the thread and ‘m’ is th is the tension applied to the thread and ‘m’ is the mass per unit mass per unit length of thread. length of thread.If ‘p’ loops are formed in the length ‘L’ of the t If ‘p’ loops are formed in the length ‘L’ of the thread,

PROCEDURE- • Find the weight of pan P and arrange the apparatus as shown in figure. • Place a load of 4 To 5 gm in the pan attached to theto the end ofthe string passing over the pulley passing over the pulley.Excite the tuning fork by switching on the power supply. Adjust the position of the pulley so that the string is set into resonant vibrations and well defined loops are obtained. If vibrations and well defined loops are obtained.If necessary, adjust the tensions by adding weights in the pan slowly and gradually.

For gradually add finer adjustment, addmilligram weight so that nodes are reduced to points. points. • Measure the length of say 4 loops formed in the middle part of the string. If string. If ‘L’ is the distance in which 4 loops are formed, then distance between two consecutive nodes is L/4. distance between two consecutive nodes is L/4. •Note down the weight placed in the pan and calculate the tension T.

T Tension, T= (wt. in the pan + wt. of pan wt. in the pan )g • Repeat the experiment twice by changing the weight in the pan in steps of one gram and altering the position of the steps of one gram and altering the position of the pulley each time to get well defined loops.• Measure one meter of the thread and find its mass produced per unit length. the mass produced per unit length.

Measuring sound

Frequency (pitch) – vibrations or cycles per second (Hz, KHz)

Amplitude – size of the vibration

Loudness – perceived strength of a sound (frequency dependent)

Intensity – energy carried by a sound (dB scale)

Sound is the form of energy that is produced when things vibrate.

It propagates as an acoustic wave through solid, liquid and

gaseous states. An ideal audible sound ranges from 20 Hz and

20 kHz. The sound that has a frequency above 20kHz is known as ultrasound.

What we hear is the effect produced due to the to-and-fro motion

of the particles in any medium. The to-and-fro motion is termed as

vibration. Sound moves through a medium by alternately

contracting and expanding parts of the medium which it is

travelling through. This expansion and compression create a

minute pressure difference that we perceive as sound. Hence, it

is a mechanical wave of pressure and displacement. In other words, the sound is the thin line between Noise and Music.

Types of Sound

Sounds are of many types, depending on the pitch, loudness,

amplitude, and frequency of the sound wave, but not all of them

please our sense of hearing. Depending on whether we like it or

not, the sound is broadly classified into noise and music.

Music is what pleases our sense of hearing. It depends on

numerous factors and varies from person to person.

On the other hand, the definition of noise is hazy, it’s not clear.

The boundaries that separate musical sound from noise is

blurry. What is music to someone, can be noise to somebody

else.

Parameter Sound Noise

Definition

It is defined as the continuous vibrations that travel from one medium to another

It is defined as the unpleasant sound that causes disturbance

Effects on healthSound has a positive effect on the health

Noise has a negative effect on health like hearing loss, hypertension

Difference between Sound and Noise

Musical Sound Noise

(i) It has a pleasing effect on the ears

i) It is displeasing to the ear

(ii) It is produced by regular periodic vibrations of a body

(ii) It is produced by irregular vibrations in a material

(iii) The amplitude of vibration and its frequency do not change suddenly

(iii) The amplitude and frequency of vibration may change suddenly

Characteristics of musical sound

Pitch: The pitch is the characteristics of a musical sound which depends upon the frequency. ...Loudness: The loudness of musical sound is related to the intensity of the sound the higher is the intensity, the higher will be the loudness. ...Quality or timber: It measure the complexity of sound.

Magnetostriction method:

Principle:

The general principle involved in generating ultrasonic

waves is to cause some dense material to vibrate very

rapidly. The vibrations produced by this material than cause

air surrounding the material to begin vibrating with the same

frequency. These vibrations then spread out in the form of

ultrasonic waves.

Production of Ultrasonic waves- Magnetostriction

Oscillator

Principle: When a rod of ferromagnetic material like

nickel is magnetized.

Longitudinally, it undergoes a very small change in

length.

This is called Magnetostriction effect.

Construction:

The circuit diagram of magnetostriction ultrasonic oscillator is

as shown in the figure1.3.2.

A short permanently magnetized nickel rod is clamped in the

middle between two knife edges.

A coil L1 is wound on the right hand portion of the rod. C is a

variable capacitor.

L1 and C1 form the resonant circuit of the collector-tuned

oscillator.

Coil L2 wound on the LHS of the rod is connected in the base

circuit.

The coil L2 is used as a feed back loop.

Working:

When the battery is switched on, the resonant circuit L1C1 sets up an alternating current of frequency.

This current lowing round the coil L1 produces an alternating magnetic iels of frequency f along the length of the nickel rod. The rod starts vibrating due to magnetostrictive effect. The vibrations of the rod create ultrasonic waves.

The longitudinal expansion and contraction of the rod produces

an E.M. in the coil L2.

This e.m.f is applied to the base of the transistor.

Hence the amplitude of high frequency of high oscillations in

coil L1

is increased due to positive feedback.

The developed alternating current frequency can be turned with

the natural frequency of the rod by adjusting the capacitor.

Condition for Resonance:

Frequency of the oscillator circuit = Frequency of the

vibrating rod

Where ‘l’ is the length of the rod

‘E’ is the Young’s modulus of the rod

‘ρ’ is the density of the material of the rod.

The resonance condition is indicated by the rise

in the collector current shown in the

milliammeter.

Piezo Electric Crystals

The crystals which produce piezo-electric eect and converse Piezo electric

effect are termed as Piezo electric crystal.

Example: Quartz, Tourmaline, Rochelle Salts etc.

At typical example or a piezo electric crystal (Quartz)

It has an hexagonal shape with pyramids attached at both ends.

It consists of 3 axes. Viz.,

(i) Optic Z axis, which joins the edges of the pyramid

(ii) Electrical axis(X axis), which joins the corners of the hexagon and

(iii)Mechanical axis, which joins the center or sides of the hexagon

X-cut and Y cut crystals

X-Cut crystal:

When the crystal is cut perpendicular to the X-axis, as shown in

the figure 1.4.2, then it is called X-crystl.

Generally X-cut crystals are used to produce longitudinal

ultrasonic waves.

Y-Cut Crystal:

When the crystal is cut perpendicular to the Y-axis, as shown in

the figure 1.4.3, then it is called Y-cut crystal.

Generally, Y-Cut crystal produces transverse ultrasonic waves.

Piezoelectric Effect

Definition: When a mechanical stress is applied to

the mechanical axis with respect to optical axis, a

potential difference is developed across the electrical

axis with respect to optic axis

Inverse Piezoelectric Effect:

Definition: When an alternating electric field is

applied to electrical axis with respect to optical axis,

expansion or contraction takes place in the

mechanical axis with respect to optical axis.

Production of Ultra sonic waves – Piezo Electric Oscillator

Principle:

This is based on the Inverse piezoelectric effect. When a quartz

crystal is subjected to an alternating potential difference along the

electric axis, the crystal is set into elastic vibrations along its

mechanical axis. If the frequency of electric oscillations coincides

with the natural frequency of the crytal, the vibrations will be of

large amplitude. If the frequency of the electric field is in the

ultrasonic frequency range, the crystal produces ultrasonic waves.

Construction:

The circuit diagram is shown in the figure 1.5 It is base

turned oscillator circuit. A slice of Quartz crystal is placed

between the metal plates A and B so as to form a parallel

plate capacitor with the crystal as the dielectric. This is

coupled to the electronic oscillator through the primary coil

L3 of the transformer.

Coils L2 and L1 of oscillator circuit are taken for the

primary of the transformer. The collector coil L2 is

inductively coupled to base coil L1. The coil L1 and variable

capacitor C form the tank circuit of the oscillator.

Working:

When the battery is switched on, the oscillator produces high

frequency oscillations. An oscillatory e.m.f is induced in the

coil L3 due to transformer action. So the crystal is now

under high frequency alternating voltage.

The capacitance of C1 is varied so that the frequency of

oscillations produced is in resonance with the natural

frequency of the crystal. Now the crystal vibrates with larger

amplitude due to resonance. Thus high power ultrasonic

waves are produced.

Condition for Resonance:

Frequency of the oscillator circuit = Frequency of the

vibrating crystal

Where ‘l’ is the length of the rod

‘E’ is the Young’s modulus of the rod

‘ρ’ is the density of the material of the rod.

‘P’ = 1,2,3 …. etc for fundamental, first

overtone, second overtone etc respectively