C7. Sound - Notes from MM

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Sound Waves

Characteristics of Sound

Produced when a body vibrates and the waves reaches us through the vibrations of the particles of the surrounding medium

Needs a medium for its propagation

Infrasonic - Audible Range - Ultrasonic <20 Hz - 20 To 20,000 Hz - >20,000 Hz

Frequency (f)

Amplitude (a)

Wavelength (λ)

Time Period (T)

Velocity (V)

V = f λ

Transfer of energy - through vibration of the particles in the medium about its mean position (Kinetic to Potential energy & vice versa)

a.k.a Elastic or Mechanical waves

Reflection

Natural/Free Vibrations

No. of vibrations made by the particle in one sec

Depends on the vibrating source producing the sound

Max displacement of the particle on either side of its mean position

Distance traveled by a wave in one Time period of the particle

f = 1/T

Time taken by the particle to complete one vibration

Distance traveled by the wave in 1 sec

Depends on the properties of the medium in which the wave travels

Longitudinal waves

Transverse waves

Particles vibrate along the direction of propagation of the wave forming compressions & rarefactions in the medium

E.g. Sound Waves solid, liquid, gas (air)

Particles in medium vibrate normal to direction of wave propagation, forming crests & troughs

E.g. Sound waves in a solid & liquid surface. In surfaces that possess rigidity

Obeys laws of reflection i.e. a) Angle of Reflection = Angle of Incidence b) Incident ray, Reflecting ray & normal to point of incidence lie in the same plane

Return of a sound wave on striking a surface such as a wall, metal sheet etc back in the same medium

Does not require a smooth/shining surface

Principle used in megaphone, sound board, ear trumpet

Echo

Requires the size of reflecting surface to be greater than the wavelength of the sound wave

Sound heard after reflection from a distant object (e.g. Cliff, Hillside, Wall etc) after the original sound has ceased

Heard only if distance (d) of sound source from reflecting surface is far enough to allow the reflected sound to reach the source at least 0.1s after the original sound is heard

Intensity of sound should be such that reflected sound is sufficiently loud to be audible

Applied in Sound ranging and echo depth sounding using Ultrasonic waves

d = Vt/2 = 17m (V = 340m/s; t=0.1s)

1. If d<17m, reflected sound overlaps with original sound 2. Repeated reflections of sound will cause the reflected sound to be prolonged - Reverberation

Ultrasonic waves can 1. travel undeviated through long distances 2. Can be confined to a narrow beam 3. Not easily absorbed in a medium

By Bats, Dolphins & Fishermen

SONAR - Finding obstacles, depth of ocean (echo depth sounding)

Medical Field (Imaging human organs - Ultrasonography & heart - Echo Cardiography)

RADAR - Similar principle using electromagnetic waves (Radio waves)

Periodic vibrations of a body of constant amplitude in the absence of an external force

Period (Natural Period)/Frequency (Natural Frequency) depends on the shape and size/structure of the body

Happens only in vacuum as medium offers resistance due to which amplitude of vibration continuously decreases

Constant natural frequency and amplitude remains constant

Simple Pendulum displaced slightly from mean position

Load suspended from spring when stretched/compressed and released

Tuning fork struck against a hard rubber pad. Vibrated with a single frequency = pure note

Air column in a flute/organ pipe

Striking keys of a piano. Each key has a different thickness and under different tension, hence different natural frequencies

Plucking a string of given length stretched at its ends

Plucking a stretched string in a Sitar, Violin.

Damped Vibrations

Restoring force

Forced Vibrations

f = (1/2π) .√(g/l) where g=acc. due to gravity, l = length of pendulum

f = (1/2π) .√(K/m) where K=force of spring, m = mass of load

f ∝ 1/l where l = length of air column. Different notes created by varying length of air column , or blowing air differently

f = (1/2l).√ (T/(πr^2)d) where l = length of string, T = tension in string, d = density of string material, (πr^2)d = mass of unit length of string

I.e. frequency of note can be increased by decreasing length, increasing Tension or reducing density/mass/radius

Periodic vibrations of a body of decreasing amplitude in the presence of a resistive force

Frictional/Resistive force

Slim branch of a tree pulled and released

Tuning fork stroked on a rubber pad

Simple pendulum oscillating in air

Vibrations of a spring having a mass at its end, in air

F = ma = m(v-u)/t = mv/t i.e. F ∝ v

Comes from surrounding medium, resists motion and reduces the amplitude of the wave. Energy of the vibrating body dissipates into heat lost to the surrounding medium.

Rate of energy loss (rate of decrease in amplitude) depends on nature of medium, and shape and size of vibrating body

Vibrations of a body that take place under the influence of an external periodic force acting on it

External Periodic force aka Driving force

Body no longer vibrates with natural frequency, it gradually acquires frequency of applied external periodic force. Amplitude of forced vibrations depends on the frequency of external force

Stem of vibrating tuning fork pressed against a table top. Resulting forced vibrations have greater energy/louder

Vibrations in diaphragm of mic. sound box, with frequencies of speaker

Stringed Instruments - Vibrations in plucked strings cause forced vibrations in the air in the acoustic/hollow sound box. Surface area of air in sound box is large, so forced vibrations have greater energy and are louder. E.g. Guitar, Violin etc

Resonance

If frequency of external force != natural frequency, amplitude dies down eventually. If exactly equal to natural frequency of vibrating body, amplitude of forced vibrations becomes very large (Resonance), tends to infinity in the absence of damping force

Amplitude of forced can be kept constant by applying a driving force such that it compensates for loss of energy from damping forces. The vibrations of the body now are called sympathetic vibrations

Special case of forced vibrations when the frequency of the external periodic force applied is exactly equal to the natural frequency of the body, and the body vibrates with an increased amplitude

Resonance experiments - Using identical tuning forks (2), pendulums (4) on a rubber string, air column

Resonant vibrations of pendulums

Resonance in machine parts

String Instruments - column of air in hollow chamber (sound box) exactly equal to natural frequency of string

Tuning fork and air column

Bridges - Wind, Troops marching

Radio & TV receivers - Frequency of electromagnetic vibrations changed till it equals that of radio waves

Loudness (Subjective)

Pitch (Shrillness)

Quality (Timbre)

Characteristic by virtue of which a loud sound can be distinguished from a faint one, both having the same pitch & quality

Depends on amplitude of the wave

Intensity (Objective)

Depends on a) Intensity of sound b) Sensitivity of receiver

Directly proportional to a) Sq of amplitude b) Surface area of vibrating body c) Density of medium d) Presence of resonant bodies & Inv. proportional to Sq of distance from source

Unit = phon. Indicates an individual's perception of loudness

Level of sound expressed in decibel (dB)

Intensity of sound at a point of the medium is the amt of sound energy passing per sec normally through a unit area at that point

Proportional to a) Sq of amplitude b) Sq of frequency c) density of medium d) velocity of sound

Sensitivity of normal human hearing is max at a frequency of 1KHz

Characteristic of sound by which an acute (shrill) note can be distinguished from a grave (flat) note of the same loudness

Depends on Frequency

Characteristic of sound which distinguishes two sounds of the same loudness and pitch,, but emitted by two different instruments because of a change in their wave forms

Depends on the wave form