Sound Waves Concept Page - 6

Example

Experimental determination of speed of sound by echo

Echoes can be used to determine the speed of sound. A sound is produced from a place at a known distance (at least 50 m) from the reflecting surface. The time difference between production of sound and receiving of echo is noted. Speed of sound is calculated as:
v=2dt$v={\displaystyle \frac{2d}{t}}$

Definition

SONAR

SONAR (Sound navigation and ranging) is a method used in submarines and ships to detect far away objects and obstacles in water. It is based on the principle of reflection of ultrasound waves. It has various applications like echo depth sounding (to find the depth of the sea), detecting enemy submarine etc.
Distance (d) of an object can be obtained as:
d=vt/2$d=vt/2$ where v is speed of ultrasound and t is the time between sending the ultrasound and receiving its echo. 

Definition

Ultrasonic and supersonic

Ultrasonic is used for ultrasound waves and is defined as waves with frequency more than 20 kHz. They cannot be heard by human beings. 
Supersonic is used for objects which travel at a speed greater than the speed of sound. These objects create sonic boom (sound associated with supersonic objects) generating enormous amounts of energy sounding like an explosion.

Definition

Sonic Boom

A sonic boom is the sound associated with the shock waves created by an object traveling through the air faster than the speed of sound. Sonic booms generate enormous amounts of sound energy, sounding much like an explosion. The crack of a supersonic bullet passing overhead or the crack of a bullwhip are examples of a sonic boom in miniature.

Definition

Define subsonic, transonic, supersonic and hypersonic on the basis of Mach number and identify effects related to each

Mach number is defined as:
M=uc$M={\displaystyle \frac{u}{c}}$,
where:
1. M is the Mach number,
2. u is the local flow velocity with respect to the boundaries (either internal, such as an object immersed in the flow, or external, like a channel).
3. c is the speed of sound in the medium.

Depending upon the value of Mach number flow can be categorized as follows:
1. Subsonic: M<0.8$M<0.8$
2. Transonic: 0.8<M<1.2$0.8<M<1.2$
3. Supersonic: 1.2<M<5$1.2<M<5$
4. Hypersonic: 5<M<10$5<M<10$

Definition

Sonic Boom

When a plane travels faster than speed of sound, the plane breaks the sound barrier and produces a loud sound. This is called sonic boom.

Example

Find the phase of resultant of two superimposing sound waves

Example: Three coherent waves of equal frequencies having amplitude 10 μ m$10\mu m$, 4 μ m$4\mu m$ and 7 μ m$7\mu m$ respectively, arrive at a given point with successive phase difference of π/2$\pi /2$. Find the Phase change.

Solution:
Y1=10sinω×t$Y_1=10\sin \omega \times t$, Y2=4sin(ω×t+π/2)=4cos(ω×t)$Y_2=4\sin (\omega \times t+\pi /2)=4\cos (\omega \times t)$, Y3=7sin(ω×t+π)=−7sin(ω×t)$Y_3=7\sin (\omega \times t+\pi )=-7\sin (\omega \times t)$
By the law of superposition of waves,
Y=Y1+Y2+Y3=3sinω×t+4cosω×t=5sin(ω×t+ϕ)$Y=Y_1+Y_2+Y_3=3\sin \omega \times t+4\cos \omega \times t=5\sin (\omega \times t+\varphi )$
(Since A2=A21+A22$A^2=A_1^2+A_2^2$ )
Here,
ϕ=cos−135=sin−145$\varphi ={\cos }^{-1}{\displaystyle \frac{3}{5}}={\sin }^{-1}{\displaystyle \frac{4}{5}}$

Example

Use relation between phase difference and path difference for two superimposing sound waves

Example: Find the path difference when two sound waves having a phase difference of 60∘${60}^{\circ }$ .

Solution:
Phase difference    δ=60o=60×π180$\delta ={60}^o=60\times {\displaystyle \frac{\pi }{180}}$ radian
or, δ=π3$\delta ={\displaystyle \frac{\pi }{3}}$ radian
Let  path difference be Δx$\mathrm{\Delta }x$ 
Using  δ=2πλ×Δx$\delta ={\displaystyle \frac{2\pi }{\lambda }}\times \mathrm{\Delta }x$
 π3=2πλ×Δx⟹Δx=λ6

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