Vibrations and Waves Sine Curve Simple Harmonic Oscillation Wave descriptions Wave motion Transverse waves • A type of waves where motion of the medium is perpendicular to direction of waves. • Eg vibration in spring and water waves Longitudinal Waves The motion of medium is along the direction of motion Eg sound waves Frequency and Period • Frequency is the number of to-and-fro vibrations it makes in certain period of time • Period of vibration is the time for one complete vibration • Eg if pendulum makes 2 vibrations in 1 second means that the frequency is 2 Hz and period is ½ s. Wave Speed Wave interference • Wave interference happens when two waves meet while traveling along the same medium. The interference of waves causes the medium to take on a shape from net effect of two waves. • They form an interference pattern. Superposition Principle • This states that where two or more waves meet, the total displacement at any point is the vector sum of the displacements that each individual waves would cause at that point Standing Waves • Standing waves (also known as stationary waves) is a type of waves that are created by combining 2 waves of the same frequency and same amplitude. • Standing wave have nodes and antinodes. • Nodes are the regions of minimal or zero displacement with minimal or zero energy. Doppler Effect Doppler Effect • It is a change in frequency of the waves when the source or observer is moving. F’ = 𝑣±𝑣𝑂 F( ) 𝑣∓𝑣𝑠 Sample questions • You robbed a bank and speed away in a car at 80m/s. A police car is chasing you from behind at 95 m/s. Its siren, sounding at a frequency of 775 Hz, makes you anxious. Calculate the frequency you will hear due to motion of the cars. Sample questions • You are standing beside a lake when suddenly a scary looking goose comes running through the grass towards you at a constant speed, honking angrily. You hear a frequency of 84.0 Hz. The goose as it turns out, is not mad at you, but rather at the kid chasing its goslings, and runs straight through your legs. After it passes, you hear a frequency of 56.0 Hz. What is the speed of the goose? Blue or Red shift • Doppler effect can also happens in light. When light source approaches, there is a increase in frequency. • Increase in frequency is called blue shift and decrease in frequency is called red shift. Sound waves Sound • Most sound are caused by the vibrations of matter. • This is an example longitudinal waves. • It is made up of series of compression and rarefaction The frequency of the vibrating source and the frequency of the wave it produces are the same. Speed of Sound in Air • The speed of sound depends on wind conditions, temperature and humidity. • It does not depend on loudness or the frequency of the sound. • All sounds travelling in same medium will have same speed. • Factors affecting speed of sound • Water vapor in the air increases the speed of sound. • Sound travels faster in warm air. Reflection of Sound • The reflection of sound is called echo. Reflection of sound also depends on the surface. If surface is rigid it can reflect more sound. • When sound undergoes multiple reflection and persist after the source stop emitting, this is called reverberation. Natural and Forced Frequency • Objects are set to vibrate at their own frequency. This is a natural frequency. • The tendency of one object to force another interconnected object into vibrational motion is referred to as a forced vibration. • When there are more surface area, means more molecules will vibrate and it will also increase amplitude. Resonance • When one object vibrating at the same natural frequency of a second object forces that second object into vibrational motion. Waves Interference Beats Pitch • Musical Notes have their own pitch. We can describe pitch by frequency. Rapid vibration of sound source will produce sound of high frequency. Sound Intensity and loudness • The amount of sound energy passing each second through unit area is called the intensity of sound. Increasing the amplitude of sound wave increase the intensity. • Intensity of sound is proportional to the square of the amplitude of sound. • Unit W/m^2. • The intensity of sound produced in the ear is called loudness. It is a physiological sensation. Different person will hear different loudness. • It is measured in decibel. More on Music • Many sound of different frequency combines to form a superposition of many tones. • The various tones are called as partial tones. • The lowest frequency determines the pitch of the note. This is called a fundamental frequency. Harmonic • A partial tone whose frequency is a whole-number multiple of the fundamental frequency is called harmonics. Fourier Analysis • Fourier analysis is a technique that is used to determine which sine waves constitute a given signal, i.e., to deconstruct the signal into its individual sine waves. The result is expressed as sine wave amplitude as a function of frequency
