# Study Notes On Physics: OSCILLATIONS AND WAVES

Here we are providing the short notes on Physics which will be help to crack science part in may examinations like SSC, Railway and other competitive exams.

# OSCILLATIONS AND WAVES

Periodic Motion

• A motion which repeats itself identically after a fixed interval of time, is called a periodic motion.

For example

– Motion of arms of a clock, orbital motion of the earth around the sun, motion of a simple pendulum etc.

Oscillatory Motion

• A periodic motion taking place to and fro or back and forth about a fixed point, is called oscillatory motion.

For example

– Motion of a simple pendulum.

– Motion of a loaded spring etc.

• If a particle oscillates with its own natural frequency without help of any external periodic force. The oscillation is then called damped oscillation.
• When a body oscillates with the help of an external periodic force with a frequency different from natural frequency of the body, then oscillation is called forced oscillation.

Simple Harmonic Motion (SHM)

• An oscillatory motion of constant amplitude and of single frequency under a restoring force whose magnitude is proportional to the displacement and always acts towards mean position, is called Simple Harmonic Motion.

Characteristics of SHM

When a particle executing SHM passes through the mean position:

1. No force acts on the particle.
2. Acceleration of the particle is zero.
3. Velocity is maximum.
4. Kinetic energy is maximum.
5. Potential energy is zero.

When a particle executing SHM is at the extreme end, then:

1. Acceleration of the particle is maximum.
2. Restoring force acting on particle is maximum.
3. Velocity of particle is zero.
4. Kinetic energy of particle is zero.
5. Potential energy is maximum.

Simple Pendulum

• A heavy point mass suspended from a rigid support by means of an elastic inextensible string, is called a simple pendulum.
• Time period of a simple pendulum is given by
• The time period of a simple pendulum of infinite length is 84.6 min. The time period of a second’s pendulum is 2 s. Its length on the earth is nearly 100 cm.
• Acceleration due to gravity decreases with altitude (height) and therefore time period of a pendulum clock will increase and clock becomes slow.
• If the bob of a simple pendulum is suspended from a metallic wire, then the length of the pendulum increases with increase in temperature and therefore its time period also increases.
• A girl is swinging over a swing. If she stands up over the swing, then the effective length of the swing decreases and therefore, the time period of oscillations decreases.
• A pendulum clock cannot be used in a space-ship.

Damped Harmonic Motion

• When there is friction or any other force acting within an oscillating system, the amplitudes of the oscillation decreases over time to this damping force. This is called damped harmonic motion.

Resonant Oscillations

• When a body oscillates with its own natural frequency (V0) with the help of an external periodic force also called forced harmonic motion. And if the frequency (v) provided by the external agent is equal to the natural frequency of the body, the oscillations of the body are called resonant oscillations.

Wave

A wave is a disturbance which propagates energy from one place to the other without the transport of matter.

Waves are broadly of two types:

1. Mechanical Wave
2. Non-mechanical wave

Mechanical Wave: The waves which required material medium (solid, liquid or gas) for their propagation are called mechanical wave or elastic wave. Mechanical waves are of two types.

1. Longitudinal wave: If the particles of the medium vibrate in the direction of propagation of wave, the wave is called longitudinal wave.
2. Transverse Wave: If the particles of the medium vibrate perpendicular to the direction of propagation of wave, the wave is called transverse wave.

Waves on strings under tension, waves on the surface of water are examples of transverse waves.

Non-mechanical waves or electromagnetic waves: The waves which do not require medium for their propagation i.e. which can propagate even through the vacuum are called non mechanical wave.

Light, heat are the examples of non-mechanical wave. In fact all the electromagnetic waves are non-mechanical.

All the electromagnetic wave consists of photon.

The wavelength range of electromagnetic wave is m to  m.

Properties of electromagnetic waves

1. They are neutral (uncharged).
2. They propagate as transverse wave.
3. They propagate with the velocity of light.
4. They contains energy and momentum.
5. Their concept was introduced by Maxwell.

Following waves are not electromagnetic

1. Cathode rays
2. Canal rays
3. α rays
4. β rays
5. Sound wave
6. Ultrasonic wave

Some Important Electromagnetic Waves & their discoverer

γ-Rays   Henry Becqueral

X-Rays  W. Rontgen

Ultra-violet rays                Ritter

Infra-red rays     Hershel

Short radio waves or Hertzian Waves Heinrich Hertz

Note: Electromagnetic waves of wavelength range  m to  m are called microwaves.

Amplitude: Amplitude is defined as the maximum displacent of the vibrating particle on either side from the equilibrium position.

Wavelength: Wavelength is the distance between any two nearest particle of the medium, vibrating in the same phase. It is denoted by the Greek letter lambda. (λ)

In transverse wave distance between two consecutive crests or troughs and in longitudinal wave, distance between two consecutive compressions or rarefactions is equal to wavelength.

Velocity of wave = frequency × wavelength.

Sound

Sound waves are mechanical longitudinal waves and require medium for their propagation. It cannot propagate through vacuum. when propagated speed and wavelength changes but frequency remains constant. It is of three types:

Infrasonic waves – (0 to 20,000 Hz)

Audible waves – (20 to 20,000 Hz)

Ultrasonic waves – (>20,000 Hz)

Properties of Sound Wave

Reflection

• The bouncing back of sound when it strikes a hard surface, is called reflection of sound.
• The laws of reflection of light are also obeyed during reflection of sound.
• The working of megaphone, sound boards and ear trumpet is based on reflection of sound.
• The repetition of sound due to reflection of sound waves, is called an
• The persistence of hearing on human ear is th of a second.
• The minimum distance from a sound reflecting surface to hear an echo is nearly is nearly 17 m.
• Sound proof rooms are made of two layers of walls having vacuum between them.
• Reverberation arises due to multiple reflection of sound.
• While designing an auditorium for speech or musical concerts, one has to take proper care for the absorption and reflection of sound.
• Time taken by reverberant sound to decrease its intensity by a factor of 106 is called reverberation time.

Refraction

• When a sound wave move from one mechanical medium to another mechanical medium, it shows deviation from the original path of the incident wave. The phenomenon is called refraction. It is due to difference is speed of sound in media.

Diffraction

• When sound waves originated by a vibrating source, they spread in the medium and if the medium is homogeneous, this leads to bending of sound waves around the edges. Which is known as diffraction.
• The sound waves diffracted broadly and one can easily hears the voice of the another person.

Musical Scale

• In theory of music, a musical scale is a set of musical notes by the frequencies of which are in simple ratios to one another. Sa, re, ga, ma, pa, dha, ni is one such scale called the diatonic scale. The frequencies of these notes are: sa (256), re (288), go (320), ma (341.3), pa (384), dha (426.7) and ni (480). The next note denoted by sa has a frequency 512, twice that of sa. The interval sa-sa is called an octave (8).

Noise Reduction in Recording Media

• Five types of noise reduction system exists in recording media as discussed below

– Dolby A noise reduction system, intended for use in professional recording studios. It provided about 10 dB of broadband noise reduction.

– Dolby B was developed to achieve about 9 dB noise reduction primarily for cassettes. It was much simpler than Dolby A and therefore less expensive to implement in consumer products.

– Dolby C provides about 15 dB noise reduction.

– Dolby SR (Spectral Recording) system is much more aggressive noise reduction approach than Dolby A. Dolby SR is much more expensive to implement than Dolby B or C, but it is capable of providing upto 25 dB noise reduction in the high frequency range.

– Dolby S is found on some Hi-Fi and semi-professional recording equipment. It is capable of 10 dB of noise reduction at low frequencies and upto 24 dB of noise reduction at high frequencies.

 Doppler’s Effect The apparent change in the frequency of source due to relative motion between the source and observer is called Doppler’s effect. Applications of Doppler’s Effect The measurement of Doppler shift (based on Doppler’s effect) has been used ·         By police to check over speeding of vehicles. ·         At airports to guide the aircraft. ·         To study heart and blood flow in different parts of the body. ·         By astrophysicist to measure the velocities of planets and stars.

SONAR

• SONAR stands for Sound Navigation And Ranging. It is used to measure the depth of a sea, to locate the enemy submarines and shipwrecks.
• The transmitter of a sonar produces pulses of ultrasonic sound waves of frequency of about 50000 Hz. The reflected sound waves are received by the receiver.

Human Ear

• We are able to hear with the help of an extremely sensitive organ of our body called the ear. There are three parts of human ear

– The outer ear is called pinna. It collects the sound from the surroundings. The middle ear transmits the amplified pressure variations received from the sound wave to the inner ear.

• In the inner ear, the pressure variations are turned into electrical signals by the cochlea. These electrical signals are sent to the brain via the auditory nerve and the brain interpret them as sound.

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