Presented to :

Sir Sikandar Khan

Presented By :

Malik Armughan Hamza Ali Hamza Abbas

BEE-012 BEE-064 BEE-074

Topics : Simple Harmonic Motion

Bow & Shock Waves Sound

Simple Harmonic MotionBy Malik Armughan Bhutta

What is SHM ?

In mechanics and physics, simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement

Derivation of Equation :Let us consider a mass m attached to one end of an elastic spring which can move freely on a frictionless horizontal surface as fig 1When displaced towards right through a distance x . Fig 2

The force at that instant is given by Hooke’s law

F= kXWhere k is a constant known as Spring constantDue elasticity , spring opposes tha applied force that force is called Restoring force which is equal and opposite to applied force

F = -kx

F = -kx

The negative sign indicates that F is directed opposite to X . Towards the equilibrium position . Thus the restoring force is directly proportional to displacement x always towards equilibrium . When mass is released , it begins to oscillate about the equilibrium positionThe oscillatory motion taking place under the action of such a restoring force is known as Simple Harmonic Motion (SHM)

F = ma by comparing

-kx = ma a =-(k/m)x a α -x

The acceleration a produce in the mass m due to restoring force can be calculated using Second law of motion

“

”

The acceleration at any instant of a body executing SHM is proportional to displacement and is always directed towards its mean position

a α -x

Bow and Shock Waves

Bow Waves

A BOW waves is the wave at the bow of a ship when it moves through the waterThe size of the bow wave is a function of the speed of the ship, water depth, and the shape of the bow.The bow wave carries energy away from the ship at the expense of its kinetic energy—it slows the ship

As the bow wave spreads out, it defines the outer limits of a ship's wake. A large bow wave slows the ship down, is a risk to smaller boats, and in a harbor can damage shore facilities and moored ships. Therefore, ship hulls are generally designed to produce as small a bow wave as possible.

Shock Waves :

The waves which caused disturbance in air by any object in the shape of V is called shock waves .

The difference is bow waves produce in water and the shock waves in air

The figure shows the disturbance caused by an object (aero plane) in air .They propagate in the shape of V in the medium .

Sound Waves

Sound waves , infect are those waves which produce hearing effect in our ears.

In Physics, sound is a Vibration that propagates as a typically audible Mechanical wave of Pressure and displacement, through a medium such as air, and water.

These waves are originally the Longitudinal and Transvers waves

We generally take sound waves as longitudinal waves made by partial vibration

Propagation of Sound :Sound recovered a medium for propagation

Solid : fast speed

Liquid : Medium speed

Gas : slow speed

Vacuum : no travel

A Medium is a medium is a metiral that helps the sound (energy ) to transfer

Properties of sound :Sound has the same properties as any wave have

Loudness Pitch Interference Reflection

What is the Loudness of a Sound Wave?The loudness of a sound depends on the amplitude of the wave.The bigger the amplitude, the louder the sound.

What is the Pitch of a Sound Wave?The pitch of a sound (how high the note is)depends on the frequency of the wave.The higher the frequency, the higher the pitch.Sound is a longitudinal wave and so it isdifficult to show the amplitude and frequency on a diagram.A microphone can change the sound wave intoan alternating current that can be displayedas a transverse wave on a CRO. This makes iteasier to show the affect of amplitude and frequencyon loudness and pitch

Speed of SoundSpeed of sound can be calculated by the given formula

c= √k∕ρWhere , C is the speed of soundK is the co-efficient of stiffness (bulk modulus )ρ is the DensityThe speed of sound is approx. 343ms (1,230 km/h; 767 mph )∕

Reflection:

Reflection is the change in direction of a wavefront at an interface between two different media

Interference:

In physics, interference is a phenomenon in which two waves superpose to form a resultant wave of greater or lower amplitude.

References :

Fundamentals of Physics (by Jearl Walker clevelan state University)

Wikipedia Text Book of Physics (PTBBL)

Google Search Engine