Wave Motion Types of mechanical waves  Mechanical waves are disturbances that travel through some material or substance called medium for the waves. travel through the medium by displacing particles in the medium travel in the perpendicular to or along the movement of the particles or in a combination of both transverse waves: waves in a string etc. longitudinal waves: sound waves etc. waves in water etc.

Types of mechanical waves  Longitudinal and transverse waves sound wave = longitudinal wave C = compression R = rarefaction air compressed air rarefied

Types of mechanical waves  Periodic waves When particles of the medium in a wave undergo periodic motion as the wave propagates, the wave is called periodic. x=0 x t=0 A t=T/4 t=T period amplitude wavelength

Mathematical description of a wave  Wave function The wave function describes the displacement of particles in a wave as a function of time and their positions: A sinusoidal wave is described by the wave function: sinusoidal wave moving in +x direction angular frequency velocity of wave, NOT of particles of the medium wavelength period sinusoidal wave moving in -x direction v->-v phase velocity

Mathematical description of a wave  Wave function (cont’d) x=0 x t=0 t=T/4 t=Tperiod wavelength

Mathematical description of a wave  Wave number and phase velocity wave number: The speed of wave is the speed with which we have to move along a point of a given phase. So for a fixed phase, phase phase velocity

Wave interference, boundary condition, and superposition  The principle of superposition When two waves overlap, the actual displacement of any point at any time is obtained by adding the displacement the point would have if only the first wave were present and the displacement it would have if only the second wave were present:

Standing waves on a string  Superposition of two waves moving in the same direction  Superposition of two waves moving in the opposite direction

Sound waves  Sound Sound is a longitudinal wave in a medium The simplest sound waves are sinusoidal waves which have definite frequency, amplitude and wavelength. The audible range of frequency is between 20 and 20,000 Hz.

Pressure amplitude and ear  Pressure amplitude for a sinusoidal sound wave Pressure: Pressure amplitude:  Ear

Sound level (Decibel scale)  Decibel scale As the sensitivity of the ear covers a broad range of intensities, it is best to use logarithmic scale: Definition of sound intensity: ( unit decibel or dB) Military jet plane at 30 m Threshold of pain1201 Whisper Hearing thres. (100Hz) Sound intensity in dB Intensity (W/m 2 )

Standing sound waves  Sound wave in a pipe with two open ends

Standing sound waves  Standing sound wave in a pipe with two open ends

Standing sound waves  Sound wave in a pipe with one closed and one open end

Standing sound waves  Standing wave in a pipe with two closed ends Displacement

Resonance  Resonance When we apply a periodically varying force to a system that can oscillate, the system is forced to oscillate with a frequency equal to the frequency of the applied force (driving frequency): forced oscillation. When the applied frequency is close to a characteristic frequency of the system, a phenomenon called resonance occurs. Resonance also occurs when a periodically varying force is applied to a system with normal modes. When the frequency of the applied force is close to one of normal modes of the system, resonance occurs.

Interference of waves  Two sound waves interfere each other constructive destructive d1 d2

Beats  Two interfering sound waves can make beat Two waves with different frequency create a beat because of interference between them. The beat frequency is the difference of the two frequencies.

Doppler effect  Moving listener Source at rest Listener moving right Source at rest Listener moving left

Doppler effect  Moving source When the source moves

EM waves