Chapter - 12 Sound

When a body vibrates the air in its neighborhood is alternately compressed and rarefied. The compressed air has higher pressure than surrounding air. It therefore pushes the air particles near it causing compression to move forward. A rarefaction or low pressure is created at the original place. These compressions and rarefaction causes particles in the air to vibrate about their mean position. The energy is carried forward in these vibration. This is how sound travels.

When the gong strikes the bell, vibrations are produced in the bell which are transmitted through the air to our ears. These vibration produce sensation of sound in our ears.

Sound waves are called mechanical waves because they need a material medium to travel.

On the moon, sound cannot travel as there is no atmosphere. Sound cannot travel in vacuum so we will not be able to hear any sound.

1. Loudness is determined by the amplitude of the sound. Greater the amplitude more will be the loudness.
2. Pitch is determined by frequency. Higher is the frequency, greater will be the pitch.

Guitar

Wavelength: The distances between two consecutive compressions or rarefaction of a wave. Its S.I unit is meter.

Frequency: One compression and one rarefaction constitutes one vibration. The number of vibration in a second is called frequency. Its unit is Hertz.

Amplitude: When waves are produced, the particles vibrate about their mean position. The maximum displacement from its mean position of a particle is called its amplitude. It is measured in meters.

Time period: The time taken by the wave to complete one oscillation i.e., the time between two consecutive compressions or rarefactions is called time period.

Speed = Wavelength x frequency
V = λ × ν

f = 220 Hz, V = 440 m/s

λ = $\frac{V}{f} = \frac{440}{220} = 2m$

ν = 500 Hz.

Therefore T = $\frac{1}{500}s = 0.002s$

Loudness and intensity both depend upon the amplitude of sound. But loudness is the physiological response of our ears to a particular frequency. Our ears are more sensitive to some frequencies as compared to others. Intensity is the amount of sound energy passing per second per unit area. It is proportional to square of amplitude.

Sound travels faster in iron and slowest in air.

Time for echo = 3 s

v = 342 m/s
Therefore distance: d = v × t = 342×3 m = 513 m.

The ceilings of concert halls are curved so that after reflections from the surface, sound can reach each and every part of the hall.

Audible range 20 Hz − 20,000 Hz

1. Infra-sound less than 20 Hz
2. Ultra-sound greater than 20, 000 Hz.

t = 1.02 s, v = 1531 m/s
distance d = v × t = 1531×1.022 m = 780.81 m

Sound is a form of energy and it is produced due to vibrations of different types of object.

For example: A vibrating tuning fork, a bell, wires in a sitar and a guitar etc.

If we blow a horn, speak, or produce sound by an object in air we are pushing the air molecules. These molecules, in turn, push the adjacent molecules which impart their energy to the next ones. After losing energy in the interaction, the molecule is back to its original (mean position. This results in formation of compressions and rarefactions.

Take an electric bell and an airtight glass bell jar. The electric bell is suspended inside the airtight bell jar. The bell jar is connected to a vacuum pump, as shown in following figure. Now, if we press the switch, we will be able to hear the bell.

Now start the vacuum pump. When the air in the jar is pumped out gradually, the sound becomes fainter, although the same current is passing through the bell.

After some time when less air is left inside the bell jar you will hear a very feeble sound. At the end, when all the air is removed completely, we will not be able to hear the sound of bell. This shows sound requires material medium.

A sound wave is called a longitudinal wave because it travels in the form of compressions and  rarefactions in the medium, where the particles of the medium vibrate in a direction which is parallel to the direction of propagation of the sound wave.

The timbre of sound is that characteristic which enables us to distinguish one sound from the other even when these are of the same pitch and loudness. Each person has its own timbre of sound and this characteristic helps us to identify a person from others even without looking at him (i.e., in a dark room).

The flash of light is seen earlier than the thunder of sound even though both are produced simultaneously because the speed of light (c) is greater than speed of sound (v) by 10⁶ as $\frac{c}{v}$

$=\frac{3 \times {10}^6 m/s}{340 m/s} \simeq {10}^6$

Given,    v₁  =  20 Hz 

v₂= 20 kHz = 20 x 10 ³ Hz, and

Speed of sound, v= 344 m/s

Clearly,  ${\lambda }_1=\frac{v}{v_1} = \frac{344}{20} = 17.2m$

${\lambda }_{2 } = \frac{v}{v_2} = \frac{344}{20 \times {10}^3} = 0.0172m$

Speed of sound in air = 346 m/s and

Speed of sound in aluminium = 6420 m/s

Since time taken by sound to travel a given distance in a medium is inversely proportional to its speed in that medium,

$$\begin{gathered} \therefore \frac{time taken by sound wave to travel in air}{time taken by air to travel same dis\tan ce in aluminium} \\ =\frac{6420}{346} = 18.55 \end{gathered}$$

Since the frequency of the source of sound is 100 Hz,

Number of vibrations of the source in I second = 100

Number of vibrations of the source in I minute (i.e., 60 second) = 6000

Yes, sound follow the same laws of reflection as light does.

The laws of reflection of sound are as follows:

1. The incident sound wave, the reflected sound wave, and the normal at the point of incident all lie in the plane.
2. The angle of incidence of sound wave and angle of reflection of sound wave to the normal are equal.

In any medium as we increase the temperature the speed of sound increases. For example, the speed of sound in air is 331 m/s at 0^oc and 344 m/s at 22^oc. So, on a hotter day, we cannot here the echo between the same distances.

The practical applications of sound are as follows:

• Megaphones or loudhailers are based on multiple reflections of sound.  
• Stethoscope is a medical instrument used for listening to sounds produced within the body is also based on multiple reflection of sound.

During the downward motion of stone

Initial velocity       u = 0 m/s

Height                    h = 500 m

Acceleration           g = 10 m/s²

using the equation, $h = ut + \frac{1}{2}g{t}^2$

$500 = \left(0\right)t + \frac{1}{2}\left(10\right)t^2$

t²  = 100,

t =10

So, stone takes 10 seconds to pond from the top of the tower. Now a sound of splash is produced.

Now the time taken by the sound from base of tower to top of tower is given by

$$\begin{gathered} time = \frac{dis\tan ce}{speed} \\ \Rightarrow time = \frac{500}{340} = 1.47seconds \end{gathered}$$

So, the total time taken = 10 seconds + 1.47 seconds = 11.47 seconds

We know that, Frequency = Speed/Wavelength

Here, Speed = 339 m/s

Wavelength = 1.5 cm = 0.015 m

Therefore,

Frequency = 339/0.015 = 22600 Hz

It is not audible (as the audible frequency is 20 Hz to 20000 Hz).

A sound created in a big hall will persist by repeated reflection from the walls until it is reduced to a value where it is no longer audible. The repeated reflection that results in this persistence of sound is called reverberation.

To reduce reverberation, the roof and walls of the auditorium are generally covered with sound-absorbent materials like compressed fibreboard, rough plaster or draperies. The seat materials are also selected on the basis of their sound absorbing properties.

The loudness (or softness) of a sound is determined by its amplitude. If amplitude is higher, it is a louder sound. It depends upon the force with which an object is made to vibrate.

Bats can produce and hear sound of frequency up to 100 kHz. The sound produced by flying bat gets reflected from its prey in front of it. By hearing this reflected sound, it can detect the prey even during nights.

To clean any objects, it is placed in a cleaning solution and ultrasonic waves are sent into the solution. Due to the high frequency, the particles of dust, grease and dirt get detached and drop out. The objects thus get thoroughly cleaned.

Sonar consists of a transmitter and a detector and is installed in a boat or a ship, as shown in following figure.

The transmitter produces and transmits ultrasonic waves. These waves travel through water and after striking the object on the seabed, get reflected back and are sensed by the detector. The detector converts the ultrasonic waves into electrical signals which are appropriately interpreted. The distance of the object that reflected the sound wave can be calculated by knowing the speed of sound in water and the time interval between transmission and reception of the ultrasound. If the time interval between transmission and reception of ultrasound signal be t and the speed of sound through seawater be v. The total distance, 2d travelled by the ultrasound is then, 2d = v x t.

The sonar technique is used to determine the depth of the sea and to locate underwater hills, valleys, submarine, icebergs, sunken ship etc.

Total distance travelled by sound = 2 x 3625 = 7250 m

Time taken = 5 seconds

Therefore, speed = distance / time

= 7250 / 5 m/s

= 1450 m/s

So, the speed of sound in water is 1450 m/s.

Ultrasounds can be used to detect the defect in metal blocks. The cracks or holes inside the metal blocks, which are invisible from outside reduces the strength of the structure. Ultrasonic waves are allowed to pass through the metal block and detectors are used to detect the transmitted waves. If there is even a small defect, the ultrasound gets reflected back indicating the presence of the flaw or defect, as shown in following figure.

The outer ear is called 'pinna'. It collects the sound from the surroundings. The collected sound passes through the auditory canal. At the end of the auditory canal there is a thin membrane called the ear drum or tympanic membrane. When a compression of the medium reaches the eardrum the pressure on the outside of the membrane increases and forces the eardrum inward.

Similarly, the eardrum moves outward when a rarefaction reaches it. In this way the eardrum vibrates. The vibrations are amplified several times by three bones (the hammer, anvil and stirrup) in the middle ear. The middle ear transmits the amplified pressure variations received from the sound wave to the inner ear. In the inner ear, the pressure variations are turned into electrical signals by the cochlea. These electrical signals are sent to the brain via the auditory nerve, and the brain interprets them as sound.