Sound Waves Concept Page - 5

Definition

Units of amplitude,frequency and time-period

Unit of amplitude (A) is m$m$.
Unit of Time period (T) is s$s$.
Unit of frequency (f) is Hz$Hz$ (hertz) or s−1$s^{-1}$

Definition

Loudness of sound

Loudness is a sensation of how strong a sound wave is at a place. It is always a relative term. It is a dimensionless quantity. Its unit is decibel (dB). It is given by:
L=log(I)$L=log(I)$
where I:$I:$ Intensity of sound.
Difference of loudness, L2−L1=10log10(I1I0)$L_2-L_1=10lo{g}_{10}\left({\displaystyle \frac{I_1}{I_0}}\right)$
Note:I∝A2$I\propto A^2$ where A:$A:$ amplitude.

Definition

Echo

Echo is the sound heard after reflection from a distant obstacle after the original sound has ceased. It is often heard at high altitudes because of the large distances between the mountains.

Example

Solve problems on echos of sound waves

Example: A person is in between two vertical mountains. The person fires a gun then hears the first  echo from the nearby mountain in a time 3 s and hears second echo from far mountain in a time 4 s. The person hears the third echo after how long?

Solution:
Distance travelled by sound waves for echo 
2x=speed of sound×time of echo$2x=speedofsound\times timeofecho$
x=ϑs×32$x={\displaystyle \frac{{\vartheta }_s\times 3}{2}}$---(1)
Distance traveled by sound waves for echo 2
2(d−x)=speed of sound×time of echo2$2(d-x)=speedofsound\times timeofecho2$
2d−2x=ϑs×4$2d-2x={\vartheta }_s\times 4$ ---(2)
now putting value of 2x from (1)in (2)
2d−ϑs×3=ϑs×4$2d-{\vartheta }_s\times 3={\vartheta }_s\times 4$
2d=7ϑs$2d=7{\vartheta }_s$
Distance traveled by sound wave for echo  3
2d=ϑs×(time of echo3)$2d={\vartheta }_s\times (timeofecho3)$
2dϑs=time of echo3$\frac{2d}{{\vartheta }_s}=timeofecho3$
from (3) 2dϑs=7${\displaystyle \frac{2d}{{\vartheta }_s}}=7$
so,time of third echo is 7 seconds.

Definition

Calculate the minimum distance required to hear an echo

Example:
What should be the minimum distance between the listener and the reflector to hear an echo of sound propagating with a speed v$v$  ms−1$m{s}^{-1}$?

Solution:
If there is a sound reflector at a distance d$d$  from the source, then the time interval between original sound and its echo at the site of the source is given as:
 T=2dv$T={\displaystyle \frac{2d}{v}}$ 

⟹d=v×t2=v×12×10$⟹d={\displaystyle \frac{v\times t}{2}}={\displaystyle \frac{v\times 1}{2\times 10}}$ as Time =t=0.1s$=t=0.1s$.

Hence, d=v20$d={\displaystyle \frac{v}{20}}$.

Result

Minimum distance required to hear an echo

An echo is heard only if the distance between the person producing sound and the rigid obstacle is long enough to allow the reflected sound to reach the person atleast 0.1 second after the original sound is heard. Otherwise, the echo is not distinguished even on reaching the ears. This value can be calculated and comes out to be 17.2 m for air and 70 m for water.

Example

Applications of echoes

Echoes are used by bats, dolphins and fisherman to detect an object / obstruction.
They are also used in SONAR (Sound navigation and ranging) and RADAR(Radio detection and ranging) to detect an obstacle. SONAR employs the detection of reflections of ultrasonic waves for the detection of an object whereas RADAR employs the detection of reflections of radio waves for the detection of an object.
Echoes also find applications in medical science like ultrasonography and echo cardiography for imaging of human organs. 

Definition

Working and applications of RADAR

Ultrasonic wave requires a material medium for its propagation. When an artificial satellite has to be tracked ultrasonic waves cannot be used as it cannot travel in vacuum. More over the ultrasonic wave loses its energy to the medium in which they travel. As a solution to these problems a new technique called RADAR was developed. It is an acronym of Radio Detection and Ranging. It works very similar to that of SONAR, but electromagnetic wave used in the place of ultrasonic wave.In 1886 a German Physicist Heinrich Hertz showed that radio waves could be reflected from metallic objects.This discovery led to the development of Radar. Radar is an object detecting system which uses electromagnetic wave specially radio wave to determine the range, altitude, direction or speed of both moving and fixed objects. 

Definition

Reverberations

A sound created in a big hall persists by repeated reflections from the walls until it is reduced in intensity to an undetectable value. The repeated reflections that results in the persistence of sound are called reverberations. They are undesirable as the reflections interfere among themselves and make the sound difficult to understand. Reverberations are reduced by reducing the reflections from the walls of large halls by covering them by sound-absorbent materials like rough plaster and fibreboard. 

Example

Uses of multiple reflections of sound

Uses of multiple reflections of sound are:

• Sound producing devices that uses a conical shape like megaphones to increase the intensity of sound waves in particular directions.
• Stethoscope: Sound undergoes multiple reflections in the wires of the stethoscope.
• Curved ceilings of halls and use of soundboards to evenly distribute the sound across the hall. 

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