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Multiple choice physics study of sound types of waves sound as a wave of disturbance sound waves are longitudinal waves

In brass, the velocity of longitudinal waves is $100\ times$ the velocity of transverse waves. If $Y = 1 \times 10 ^ { 11 }\ N/m^2,$ then the stress in the wire is

  1. $10 ^ { 7 }/ N/m^2$
  2. $10 ^ { 8 }/ N/m^2$
  3. $10 ^ { 9 }/ N/m^2$
  4. $10 ^ { 10 }/ N/m^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Velocity of transverse wave ${V _T} = \sqrt {\left( {\frac{T}{m}} \right)} $

${V _T} = \sqrt {\left{ {\frac{T}{{\left( {\pi {r^2}\rho } \right)}}} \right}} .............\left( 1 \right)$
Velocity of longitudinal wave ${V _L} = \sqrt {\frac{Y}{\rho }} ...............\left( 2 \right)$
Given:
$\begin{array}{l} { V _{ L } }=100{ V _{ T } } \ \therefore \sqrt { \frac { Y }{ \rho  }  } =100\sqrt { \left{ { \frac { T }{ { \left( { \pi { r^{ 2 } }\rho  } \right)  } }  } \right}  }  \ \therefore Y={ \left( { 100 } \right) ^{ 2 } }\times \left{ { \frac { T }{ { \left( { \pi { r^{ 2 } } } \right)  } }  } \right}  \end{array}$
As stress $ = \left{ {\frac{{\left( {force} \right)}}{{\left( {area} \right)}}} \right} = \left{ {\frac{T}{{\left( {\pi {r^2}} \right)}}} \right}$
$\therefore Y = {10^4} \times $stress
$\therefore$ stress $ = \left( {\frac{Y}{{{{10}^4}}}} \right) = \left{ {\frac{{\left( {1 \times {{10}^{11}}} \right)}}{{\left( {{{10}^4}} \right)}}} \right} = 1 \times {10^7}\,\,N/{m^2}$

Multiple choice physics study of sound types of waves sound as a wave of disturbance sound waves are longitudinal waves

Choose the correct options for longitudinal wave

  1. maximum pressure variation is BAk

  2. maximum density variation is pAk

  3. pressure equation and density equation are in phase

  4. pressure equation and displacement equation are out of phase
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In a longitudinal wave, the pressure variation and density variation are both proportional to the displacement gradient, causing them to be in phase with each other.

Multiple choice physics study of sound types of waves sound as a wave of disturbance sound waves are longitudinal waves

Find the incorrect statement

  1. Ultrasound can be used to determine the sex of the unborn baby (embryo)

  2. Ultrasound can be used to keep away rodents in cold storage

  3. Ultrasound can be used to detect even bone fractures

  4. Ultrasound travels faster than sound
Reveal answer Fill a bubble to check yourself
C,D Correct answer
Explanation

Ultrasound frequency used for imaging is about $5 MHz.$
The corresponding wavelength is $\lambda = \dfrac{v}{\nu}=\dfrac{1540 \text{m/s}}{5\times 10^6} = 0.3mm$ 
Here speed of ultrasound in tissue is taken to be $1540 m/s$.
So ultrasound can not be used for bone fractures as it bone fracture can have size of few microns.
Ultrasound does not travel faster than sound. Sound speed does not depend on frequency.
$v=\nu \lambda$ if $\nu$ is higher, $\lambda$ becomes smaller and $v$ remains constant.

Multiple choice physics study of sound types of waves sound as a wave of disturbance sound waves are longitudinal waves

A metal bar clamped at its center resonates in its fundamental mode to produce longitudinal waves of frequency 4 kHz.Now the clamp is moved to one end. If ${f _1}\;{\text{and}}\;{f _2}$ be the frequencies of first overtone and second overtone respectively then, 

  1. $3{f _2} = 5{f _1}$
  2. ${f _2} = 2{f _1}$
  3. $3{f _1} = 5{f _2}$
  4. $2{f _2} = {f _1}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\begin{array}{l} { f _{ 1 } }=3f \ { f _{ 2 } }=5f \ \Rightarrow 5{ f _{ 1 } }=3{ f _{ 2 } } \ Hence, \ option\, \, A\, \, is\, \, correct\, \, answer. \end{array}$

Multiple choice physics study of sound types of waves sound as a wave of disturbance sound waves are longitudinal waves

In a stationary wave represented by $y = a \sin wt \cos kx$, amplitude of the component progressive wave is

  1. $\frac{a}{2}$
  2. $a$
  3. $2a$
  4. $a^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A stationary wave y = a sin(wt) cos(kx) can be written as the sum of two progressive waves: y = (a/2) sin(wt - kx) + (a/2) sin(wt + kx). Therefore, the amplitude of each component wave is a/2.

Multiple choice physics study of sound types of waves sound as a wave of disturbance sound waves are longitudinal waves

Which of the following equations represents a wave travelling along  $Y$-axis ?

  1. $x = A \sin ( k y - \omega t )$
  2. $y = A \sin ( k x - \omega t )$
  3. $y = A \sin k y \cos \omega t$
  4. $y = A \cos k y \sin \omega t$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A wave traveling along the Y-axis must have its displacement as a function of (y +/- vt). Option A represents a wave where the displacement x is a function of (y - vt).