Sound

Variation of velocity of sound in a gas with temperature.
    
The velocity of sound in a gas v =   
          ()
                     
Where M is molecular weight of gas and T is absolute temperature of the gas
       =   
   
   
 
 
 
Vt = V₀     v₀ = 332m/s
  
Vt = V₀ +0.61t⁰C
Note: 
1. The velocity of sound in air increases by 0.6m/s for every 1⁰C rise of temperature.
2. Velocity of sound in a gas is directly proportional to the square root of the absolute temperature   
3. But from kinetic theory of gases rms velocity of gaseous molecular is V_rms =  
     
   
    
 velocity of sound in a gas is of the order of the velocity of its molecules
The velocity of sound in gas at absolute temperatures T and T¹ are V, nv then
                
   
              
   

EFFECT OF PRESSURE:
    Since V =   
The velocity of sound in air is independent of pressure.

EFFECT OF DENSITY:
At a constat pressure the velocity of sound depends on the density of the gas 
      
      \( \frac{{v_1 }} {{v_2 }} = \sqrt {\frac{{\rho _2 }} {{\rho _1 }}} \)

Variation with humidity:-
1. With increase in humidity, density of air decreases. So with increase of humidity velocity of sound increases.
2. Sound travels faster in humid air (rainy season) than in dry air at the same temperature.
    P_{moist air}< P_{dry air}
     V _{moist air} < V_{dry air}
Note:- Amplitude frequency, phase, loudness, pitch quality etc... Have practically no effect on velocity of sound.

Velocity of sound in a solid:-
The velocity of sound in solids is v = \( \sqrt {\frac{y} {\rho }} \)
Where y - is young's modulus of the material velocity of sound in steel is greater than in copper or brass (or) silver.

Velocity of sound in a liquid:-
Velocity of sound in liquids V = \( \sqrt {\frac{k} {\rho }} \)  
Where k is the bulk modulus of the liquid. 

ECHO:
In acoustics, an echo is a reflection of sound that arrives at the listener after bouncing off a surface. It occurs when sound waves encounter a hard and reflective object, such as a wall, building, or mountain, and are then reflected back to the listener. The delay between the original sound and its reflection creates the perception of an echo.

Key characteristics of echoes include:

Reflection: Echoes result from the reflection of sound waves. When sound encounters a reflective surface, the waves bounce off the surface and travel back to the listener.

Distance and Delay: The distance between the source of the sound and the reflecting surface, as well as the distance back to the listener, determines the time delay of the echo. The farther the reflecting surface, the longer the delay 
between the original sound and its reflection

Reverberation: In some cases, multiple reflections of sound waves may occur, creating a series of echoes. This prolonged series of reflections is known as reverberation and is often encountered in large, acoustically reflective spaces such as auditoriums or cathedrals.

Sound Absorption: Echoes are less likely to occur in environments where sound-absorbing materials are present. Soft and porous surfaces, like curtains or acoustic panels, can absorb sound rather than reflecting it.

The formula for calculating the distance to an object that reflects sound, based on the time delay between the emission of the sound and the reception of its echo, is given by:
               \( d = \frac{{v \times t}} {2} \)             
where:
d is the distance to the reflecting object,
v is the speed of sound in the medium (air, for example),
t is the time delay between the emission of the sound and the reception of its echo.