Tag: standing waves

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Questions Related to standing waves

Multiple choice standing waves waves physics

The equation of a traveling and stationary wave are ${ y } _{ 1 }=a sin(\omega t-kx)$ and ${ y } _{ 2 }=a \sin kx  \cos \omega t$. The phase difference between two point ${ x } _{ 1 }=\dfrac { \pi  }{ 4k }$ and $ { x } _{ 2 }=\dfrac { 4\pi  }{ 3k } $ are ${ \phi  } _{ 1 }$ and ${ \phi  } _{ 2 }$ respectively for two waves where k is the wave number, the ratio of ${ \phi  } _{ 1 }/{ \phi  } _{ 2 }$ 

  1. 6/7

  2. 16/3

  3. 12/13

  4. 13/12
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice standing waves waves physics

A standing wave pattern is formed on a string. One of the waves is given by equation  $Y _ { 1 } a \cos ( \omega t - K X + \pi / 3 )$  then the equation of the other wave such at  $X = 0$  a noode is formal

  1. $y _{ 2 } = \operatorname { a sin } \left( \omega t + K X + \dfrac { \pi } { 3 } \right)$
  2. $y _ { 2 } = a \cos \left( \omega t + K X + \dfrac { \pi } { 3 } \right)$
  3. $y _ { 2 } = a \cos \left( \omega t + K X + \dfrac { 2 \pi } { 3 } \right)$
  4. $y _ { 2 } = a \cos \left( \omega t + K X + \dfrac { 4 \pi } { 3 } \right)$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a standing wave formed by two waves y1 and y2, if a node exists at x=0, the resultant wave must be zero at x=0 for all t. This requires y1 + y2 = 0 at x=0. Given y1 = a cos(wt - kx + pi/3), at x=0, y1 = a cos(wt + pi/3). Thus, y2 must be -a cos(wt + kx + pi/3), which is equivalent to a cos(wt + kx + pi/3 + pi) = a cos(wt + kx + 4pi/3).

Multiple choice standing waves waves physics

Two simple harmonic waves of amplitude 5 cm and 3 cm and of the same frequency travelling with the same speed in opposite directions superpose to produce stationary waves. The ration of the amplitude at a node to that at an antinode in the resultant wave is

  1. zero

  2. infinity

  3. 5:3

  4. 1:4
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice standing waves waves physics

The equation of stationary wave is given by $y=5\, cos (\pi x/3)\, sin 40 \pi t$ where y and x are given in cm and time t in second. Then a node occurs at the following distance 

  1. 3 cm

  2. 10 cm

  3. 5 cm

  4. 1.5 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Nodes occur where the spatial part of the stationary wave equation equals zero, meaning cos(pi x / 3) = 0. This happens when pi x / 3 = pi/2, 3pi/2, etc., which yields x = 1.5 cm for the first node. Thus, 1.5 cm is the correct position for a node.

Multiple choice standing waves waves physics

A $string$ is stretched between fixed points separated by $75.0\ cm$. It is observed to have resonant frequencies of $420\ Hz$ and $315\ Hz$. There are no other resonant frequencies between these two.
Then, the lowest resonant frequency for this string is :

  1. $1.05$Hz
  2. $1050$Hz
  3. $10.5$Hz
  4. $105$Hz
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given,  $\dfrac { nV }{ 2L } =315\quad \longrightarrow (1)$

     &     $\dfrac { \left( n+1 \right) V }{ 2L } =420\quad \longrightarrow (2)$
equation (2) $-$ equation (1), we get
$\dfrac { \left( n+1 \right) V }{ 2L } -\dfrac { nV }{ 2L } =420-315$
$\Rightarrow \quad \left[ \dfrac { V }{ 2L } =105\quad { H } _{ 3 } \right] \rightarrow $  Lowest possible resonant frequency

$\therefore $  Option (D) is correct.

Multiple choice standing waves waves physics

A wave represented by $y=2 cos (4x-\pi t)$ is superposed with another wave to form a stationary wave such that the point x= 0 is a node. The equation of other wave is:

  1. $2 sin(4x+\pi t)$
  2. $-2 cos (4x -\pi t)$
  3. $-2 cos (4x +\pi t)$
  4. $-2 sin (4x -\pi t)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to options

If $y _2=-2\cos(4x+\pi t)$
Then, when superimposed,
$y=y _1+y _2\ \quad 2\cos(4x-\pi t)-2\cos(4x+\pi t)\ =2[2\sin(\cfrac{(4x-\pi t)+(4x+\pi t)}{2})\sin(\cfrac{(4x-\pi t)-(4x+\pi t)}{2})]\ \quad=2[2\sin(4x)\sin(-\pi t)]\y=-4\sin(4x)\sin(\pi t)$
at $y=0\Rightarrow y=0$ (i.e node)

Multiple choice physics oscillations and waves standing waves in strings standing waves reflection of waves

A string is under tension so that its length is increased by $1/n$ times its original length. The ratio of fundamental frequency of longitudinal vibrations and transverse vibrations will be

  1. $1:n$
  2. ${n}^{2}:1$
  3. $\sqrt{n}:1$
  4. $n:n+1$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The frequency of longitudinal vibrations depends on the speed of sound in the material, while transverse vibrations depend on tension. Calculating the ratio based on the extension 1/n leads to the n/(n+1) relationship.

Multiple choice physics oscillations and waves standing waves in strings standing waves reflection of waves

Motion that moves to and fro in regular time intervals is called _________________ motion.

  1. Vibratory

  2. Translatory

  3. Rotatory

  4. Accelerating
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Sounds are made by vibrations. Some vibrations are easy to see. The vibrations that create sound must travel through a medium, such as air or water, or anything made of molecules. With each forward motion, air molecules pulse outward, pushing other air molecules and crowding them together. With each backward motion, the molecules get less crowded. The forward and backward vibration of the glass creates a chain reaction of crowded and not-so-crowded molecules that ripples through the air. This traveling vibration is called a sound wave. 
Motion that moves to and fro in regular time intervals is called vibratory or oscillatory motion.

Multiple choice physics oscillations and waves standing waves in strings standing waves reflection of waves

When we hear a sound, we can identify its source from : 

  1. Amplitude of sound

  2. Intensity of sound

  3. Wavelength of sound

  4. Overtones present in the sound
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Answer is D.

When we hear a sound, we can identify its source from overtones present in the sound.
The fundamental is the frequency at which the entire wave vibrates. Overtones are other sinusoidal components present at frequencies above the fundamental. All of the frequency components that make up the total waveform, including the fundamental and the overtones, are called partials. Together they form the harmonic series.
Overtones which are perfect integer multiples of the fundamental are called harmonics. When an overtone is near to being harmonic, but not exact, it is sometimes called a harmonic partial, although they are often referred to simply as harmonics. Sometimes overtones are created that are not anywhere near a harmonic, and are just called partials or inharmonic overtones.