Wave Motion and Sound PDF

TOPIC 5: WAVE MOTION AND SOUND WAVE MOTION When energy is transferred by the passage of a periodic disturbance through an elastic medium, it is said to be in Wave Motion. The **maximum amplitude** is at the region of **maximum density, called a compression**, and the **minimum amplitude** is at t...

TOPIC 5: WAVE MOTION AND SOUND WAVE MOTION When energy is transferred by the passage of a periodic disturbance through an elastic medium, it is said to be in Wave Motion. The **maximum amplitude** is at the region of **maximum density, called a compression**, and the **minimum amplitude** is at the region of **minimum density, called a rarefaction.** These are called **compression or longitudinal** waves and are a set of pulses through a medium. **Sound waves** are compression waves because they use the **mechanical action of molecules** to transfer their action through a medium. For this reason**, sound waves cannot travel through a vacuum.** **Light waves** are different again. They are the type of **Electromagnetic Radiation that is detectable by the human eye.** **They are not mechanical waves**, but they display similar behaviour, and **are able to travel through vacuum.** Properties of Waves All waves have an amplitude, a **wavelength, a frequency and a period.** **Amplitude** distance between crests (maximum displacement) and troughs, (minimum displacement) **Wavelength λ "lambda** **Frequency f** - the number of wavelengths occurring per second. The period is the time taken for one cycle to complete and equals 1/f The speed of energy propagation is V and given by V = λf Reflection and Refraction A system of waves will change direction when it changes speed for any reason. (Refraction). If the system encounters a solid barrier, the energy will be reflected. Diffraction If the obstacle has an edge then the wave system will "bend" and start a new system at that point. This explains how we can hear around corners. The nature of light waves has been proven by experiments showing the diffraction of light. Interference Phenomena (Superposition) When waves converge, their effect is algebraically added. For example, if a sine wave is overlaid on another sine wave of identical amplitude and frequency, it will produce a sinusoidal wave of same frequency but double the amplitude. Similarly, if a sine wave was overlaid on another sine wave exactly half a phase out of synchronisation, the result would be the two waves would cancel themselves out. STANDING WAVES Standing waves are formed when a wave interferes with its own reflection This will occur when the medium is secured at both ends like a guitar string or a structural member. **The resultant** is merely the **result of the two individual waves** - the blue wave and the green wave - added together in accordance with the principle of superposition. The point where the standing wave has **no amplitude is called the node**, and the point of **maximum amplitude is called the antinode.** **Standing waves** are formed when **a fundamental wave** (the longest wavelength that can fit in a tube or on a string) is subjected to **interference and a harmonic wave is produced** (a multiple of the original, fundamental wave). **Resonance** can set up a standing wave in a piece of structure, and cause fatigue at the antinodes. Consider the following example. BEATS Suppose we tune two strings of a guitar to vibrate at almost, but not quite, the same frequency. Plucked simultaneously, the volume of the sound produced by them appears to rise and fall continuously. This rise and fall has a fixed frequency called the beat frequency. What is happening is that the sound waves produced by the two guitar strings interfere and our ears detect the variation of the resultant intensity. Maximum intensity is heard when the waves add together (interfere constructively) and minimum intensity is heard when the waves cancel each other out (interfere destructively). SOUND **Sound waves** are usually defined as **pressure waves of frequencies which our brains can interpret**. The eardrum would be affected by all pressure waves, but only those frequencies, between **20 Hz to 20,000 Hz, are "heard" by most humans**. Intensity of Sound **Intensity is determined by the amplitude of the sound wave and is measured in Watts** per metre2 , however it is more convenient to express a sound as a relative quantity called Intensity Level. The **intensity level (IL)** of sound waves is **measured** in a unit called the **decibel** (after Alexander Graham Bell). It should be noted that **120 db is the\"threshold of pain\".** Sound of this intensity is painful to the normal ear. Quality **Quality or "timbre"** of sound depends on the **nature of the harmonics present.** You will recall that harmonics are numerical multiples of the original frequency. SPEED OF SOUND Sound waves have been identified as longitudinal compression waves travelling through an elastic medium, of which air is a good example. Speed of sound in air **varies** according to **atmospheric temperature.** If the aircraft is moving at the speed of sound, then these disturbances cannot propagate away from the airframe and pile up, creating the phenomenon known as a shock wave, which is intense enough to be heard. The sonic boom. DOPPLER EFFECT When a source of sound is not moving, the sound waves radiate out from the source like ripples in a pond. When the source of sound moves, however, the frequency (and pitch) ahead of the source becomes higher than the frequency behind it. This change in frequency is called the Doppler effect. It accounts for the sound of sirens, motorbikes, and aircraft etc. becoming higher pitched as they approach, then decreasing in pitch as the vehicle passes.