Waves of Sound

                                                                                                  

Introduction 

Who doesn't love the beach? My favorite part is the sound of the waves, and being a physics student I am instantly reminded of sound waves. Sound is produced when a body vibrates, and vibration is nothing but the back and forth motion of a body about its mean (or middle) position (for example the motion of a pendulum or a swing). 

When an object vibrates, it does work on the surrounding particles by applying force (pushing) against them. Work is done so energy is transferred. Here, from the vibrating object to the particles, causing them to vibrate. From particle to particle, the energy finally reaches our ear drum causing it to vibrate. That's how we hear sound. Sound travels in the form of waves; that is, there is a transfer of energy (by vibration of particles) but no actual movement of particles. 

No sound can be heard in space. This is because space is the closest to vacuum - an empty space where there is no matter. This means that even if there are vibrating bodies producing sound, there are no particles to vibrate and transfer energy; so, sound can't travel. It needs a medium for propagation and is therefore a mechanical wave.

There are two types of waves: longitudinal and transverse. Sound is a longitudinal wave. In longitudinal waves, the particles vibrate along the direction in which the wave travels. The image shows a longitudinal wave traveling in a horizontal direction, and the particles are also vibrating horizontally (left to right). 

When the particles come closest to each other, they form compressions.This happens when a particle, after gaining energy, vibrates forward to push the next particle, thus coming close to it. When particles are farthest, they form rarefactions. This happens when the particle, after transferring its energy, begins to move back to its mean position. At the same time the next particle, after gaining energy, is moving forward; thus a large gap is created between the two. One compression and rarefaction constitute one vibration. 

Longitudinal waves travel in solids, inside liquids and in gasses. We are able to hear anybody speak through longitudinal waves in air. 

In transverse waves the particles vibrate perpendicular to the direction in which the wave travels. The image shows a transverse wave traveling in a horizontal direction while the particles are vibrating vertically (up and down). The directions are normal to each other (red and blue line in diagram).  Crests are the topmost points in a transverse wave while troughs are the lowest points. One crest and trough constitute one vibration. 

Transverse waves travel in solids and on the surface of liquids. This is because they involve a change in shape of the medium (vertical vibrations) in which they travel and thus the medium should be rigid enough to keep its shape intact. On the surface of liquids the rigidity is provided by surface tension (property of surface of liquid to acquire minimum possible area - particles are closer - surface is rigid). An ocean wave is a transverse wave! (water molecules vibrate up and down).

Some useful definitions - The amplitude of a wave is the maximum displacement of a particle of the medium on either side of its mean position. The length or distance covered by a wave in one time period (time taken to complete one vibration) of vibration of the particle of that medium is known as wavelength. Frequency of a wave is the number of vibrations made by a particle of the medium in one second (unit - Hz or per second). 

If frequency is low (less vibrations in a given time), it implies that more time is taken to complete one vibration (time period of vibration increases). Thus, wavelength increases. Frequency and wavelength are, therefore, inversely proportional.

                                               

     

          

Echoes  

                                                                                                                                   

Sound waves, like any other wave, on striking a smooth or hard surface or the boundary of another medium, bounce back into the same medium. This is called reflection of sound. An important condition - the reflecting surface should be bigger than the wavelength of the sound wave. 

In a stethoscope, the sound received reaches the earpieces after...     

An echo is just the reflected sound heard after the original sound has ceased. So, two sounds are heard. Even after the original sound ceases, the sensation of it persists in our ear for about 0.1 seconds. Thus the reflected sound should reach our ears 0.1 seconds after we hear the original sound to be distinct from it. This can happen only at a far enough from the reflecting surface. To balance the far distance, the original sound must be loud enough to be audible when it reaches our ears. The condition for reflection of sound will also apply here. The minimum distance between the reflecting surface and source of sound in air is 17 m which is calculated using the formula speed = distance/time. Speed is the speed of sound (average) in solid = 340 m/s and time is 0.1 sec. We'll get  the total distance travelled by sound - to the reflecting surface and back - so we must take half of this distance as the minimum distance. At the top of a mountain we hear an echo as all conditions are met - a far distance, a big reflecting surface. But in a small room, even if it is empty, we can't hear an echo as our distance from the walls and ceiling is less than 17m. The sound does become louder in an empty room but that's because the furniture that absorbed much of the sound has been removed. An important use of echoes is in ultrasonography. A device is used to send ultrasound waves (not audible, with frequency higher than 20 kHz) into the body which are reflected at the boundaries of organs due to change in medium from blood to tissues. The waves return back to the device as echoes and are then processed to produce an image of the organs. We use ultrasound waves in this case as they have a high frequency (thus low wavelength) causing them to diffract less - they don't bend at the corner of the object - and form clear images.  Dolphins use echoes to detect objects as it is very hard to see far away objects in water. This is because light can't travel much of a distance - it is easily absorbed by water. Dolphins emit ultrasound waves that are reflected by objects and return to the dolphin as echoes. These are interpreted to understand the location of the object and the process is known as echolocation. SONAR (Sound Navigation and Ranging) is an important use of echoes, it's like humans' echolocation. We use a device to send ultrasound waves into the ocean, which reflect from an obstacle and are received as echoes. We then calculate the distance of the object from us by measuring from the time the waves were transmitted to the time they were received and using the formula of speed (speed of sound in water is known). Resonance

Every body has a natural frequency of vibrations. When we disturb a body from its initial position, it starts to vibrate with its natural frequency. This is different for every body depending upon its size and shape. If we apply a periodic force on a body that has the same frequency as the natural frequency of the body, it causes the vibrations in the body to increase in amplitude. This phenomenon is called resonance. The increased amplitude is due to transfer of energy from the force. If the frequency of the force is more or less than the natural frequency, all energy transferred is utilised in forcing the object to vibrate at its frequency. Thus, amplitude is small.     There is a proportional relation between the amplitude and energy supplied to the body for vibration. More energy given/work done on the object, more will be its displacement and thus more will be the amplitude. In resonance, the object has a large amplitude which implies that a large amount of energy was supplied to it for vibration. It will send forth this large amount of energy into the medium causing a loud sound. Sometimes the cups, plates, etc. in a restaurant vibrate strongly due to music. This happens when the frequency of the musical sound matches the natural frequency of the items, and resonance occurs. I'm going to come back to the sea again, not waves but seashells this time :)              When we put up a seashell to our ear, we hear the sound of the sea. This can be explained by resonance. In a room there are many low-intensity (quiet) and low-frequency (deep) sound waves like that of the wind which enter the seashell, causing it to vibrate. When one of the frequencies of the room matches the natural frequencies of the seashell, resonance occurs and a loud sound is heard on putting the seashell to our ear. The sound being low frequency is similar to that of the sea. Thus, it's really not the sea, just the amplified background noise which can even be heard on putting a cup to the ear. The concept of resonant frequencies is also used in radios where we listen to different channels just by turning the knob. We are actually matching the frequency of the waves of the radio's circuit to the frequency of the waves broadcasted by the station. When we turn the knob, the natural frequency of the circuit changes. The receiver/antenna receives various radio signals and converts them to electrical signals, but the one with the matching frequency will produce most current, due to resonance, and drive the speakers. From echoes to resonance, that's just some of the many applications of sound waves. Ending this blog with Albert Einstein's words: "Match the frequency of the reality you want and you cannot help but get it. This is physics." Check your understanding with a few quick questions-:  Q The natural frequency of an oscillating object is 10 Hz. How often in seconds should you push the object to make the oscillations bigger? Q How can someone break a glass just with their voice? Q An engine is approaching a tunnel surmounted by a cliff, and emits a short whistle when 1 km away. The echo reaches the engine after 5 seconds. Calculate the speed of the engine assuming the velocity of sound to be 340m/s.   Answer to the question in the previous blog-: Q While driving on a rainy day, a person tries to make a left turn but the car continues in a straight line. What caused this phenomenon? Hint: Was it an outward force or lack of an inward force?  Due to the rain, the road must have been wet which decreased the friction between the tires and the road (no more in direct contact). The centripetal or inward force (friction) which would allow circular motion was absent. Thus, no net force acted on the car and caused it to continue in a straight line.