Tag: waves

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Questions Related to waves

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

Equation ${ y } _{ 1 }=0.1sin\left( 100\pi t+\dfrac { \pi  }{ 3 }  \right) $ and ${ y } _{ 2 }=0.1$ cos $\pi t$ The phase difference of the velocity of particle 1, with respect to the velocity of particle 2 is 

  1. $\dfrac { -\pi }{ 6 } $
  2. $\dfrac { \pi }{ 3 }$
  3. $\dfrac { -\pi }{ 3 } $
  4. $\dfrac { \pi }{ 6 } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

v1 = dy1/dt = 0.1 * 100pi * cos(100pi*t + pi/3). v2 = dy2/dt = -0.1 * pi * sin(pi*t). This question is garbled regarding the frequencies (100pi vs pi), making a standard phase difference calculation between them invalid.

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

Which of the following equations does not represent a progressive wave ?

  1. $y=Asin[\omega (t-\frac { x }{ v } )]$
  2. $y=Asin[ \frac { 2pi }{ \lambda }(vt-x)] $
  3. $y=Asin[2\pi (\frac {t}{T}-\frac { x }{ \lambda } )]$
  4. $y=Asin[2\pi (\frac {t}{T}-\frac { x }{ v } )]$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A progressive wave must be a function of (vt - x) or (t - x/v). Option D uses (t/T - x/v), which is dimensionally inconsistent if T is period and v is velocity, as t/T is dimensionless but x/v is time.

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

A traveling wave is represented by the equation $ y = \frac{1}{10} sin(60 t + 2x) $, where x and y in meters and t is in second . this represents a wave
(1) of frequency $ \frac {30}{\pi} Hz $
(2) of wavelength $ \pi m $
(3)of amplitude 10 cm
(4) moving in the positive x direction
pick out the correct statements from the above.

  1. 1, 2, 4

  2. 1, 3, 4

  3. 1, 2, 3

  4. all
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

y = 0.1 sin(60t + 2x). omega = 60, k = 2. Frequency f = omega/2pi = 60/2pi = 30/pi Hz. Wavelength lambda = 2pi/k = 2pi/2 = pi m. Amplitude = 0.1 m = 10 cm. The wave moves in negative x direction because of the + sign.

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

A wave equation which given the displacement along the Y direction is given by $y = 10^{-4} \sin (60t+2x)$ where x and y are in meters and t is time in seconds. This represents a wave 

  1. Traveling with a velocity of 30 m/s in the negative x direction
  2. Of wavelength $\pi $ metre
  3. Of frequency 30/$\pi $hertz
  4. Of amplitude $10^{ -4 }$ metre
Reveal answer Fill a bubble to check yourself
A,B,C,D Correct answer
Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

For a wave $ y= y _0 sin ( \omega t - kx ) $, for what value of $ \lambda $ , is the maximum particle velocity equal to two times the wave velocity :-

  1. $ \pi y _0 $
  2. $ 2 \pi y _0 $
  3. $ \pi y _0/2 $
  4. $4 \pi y _0 $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Particle velocity v_p = dy/dt = y0 * omega * cos(omega*t - kx). Max particle velocity = y0 * omega. Wave velocity v_w = omega/k. Given y0 * omega = 2 * (omega/k), so y0 = 2/k. Since k = 2pi/lambda, y0 = 2 / (2pi/lambda) = lambda/pi. Thus, lambda = pi * y0.

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

Two small boats are 10 m apart on a lake. Each pops up and down with a period of 4.0  seconds due  to wave motion on the surface of water. What one boat is at its highest point, the other boat is at lowest point. Both boats are always within a single cycle of the waves. The speed of the waves is : 

  1. 2.5 m/s

  2. 5.0 m/s

  3. 14 m/s

  4. 40 m/s
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If one boat is at crest and other at trough, the distance 10m is half the wavelength (lambda/2). So lambda = 20m. Period T = 4s. Speed v = lambda/T = 20/4 = 5 m/s.

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

Consider the following two equations $L=I\omega$ and $ \dfrac { dL }{ dt } =\Gamma $. In noninertial frames :

  1. both A and B are true

  2. A is true but B is false

  3. B is true but A is false

  4. both A and B are false.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In non-inertial frames, the relation L = I*omega is generally not valid due to the changing nature of the moment of inertia or frame-dependent definitions of angular momentum. However, the torque equation dL/dt = Gamma is a fundamental law of motion that holds in inertial frames, but in non-inertial frames, pseudo-torques must be included.

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

The equation $y = a \sin^2 \left(2 \pi nt - \dfrac{2\pi x}{\lambda}\right)$ represents a wave with

  1. Amplitude $a$, frequency $n$ and wavelength $\lambda$
  2. Amplitude $a$, frequency $2n$ and wavelength $2\lambda$
  3. Amplitude $a/2$, frequency $2n$ and wavelength $\lambda$
  4. Amplitude $a/2$, frequency $2n$ and wavelength $\lambda/2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using sin^2(theta) = (1 - cos(2*theta))/2, the equation becomes y = a/2 - (a/2)cos(4*pi*n*t - 4*pi*x/lambda). This represents a wave with amplitude a/2, frequency 2n, and wavelength lambda/2 (since k = 4*pi/lambda = 2*pi/lambda_new).

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

The speed of the wave travelling on the uniform circular hoop of string, rotating clockwise in absence of gravity with tangential speed $v _0$, is :

  1. $v=v _0$
  2. $v=2v _0$
  3. $v=\dfrac{v _0}{\sqrt 3}$
  4. $v=\dfrac{v _0}{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a string rotating in a circle, the wave speed relative to the string is v0. In the absence of gravity, the speed of a transverse wave on a rotating hoop is equal to the tangential speed v0.

Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

The equation $y =A\cos^2\left(2\pi\, nt -2\pi \dfrac{x}{\lambda}\right)$ represents a wave with

  1. amplitude $A/2$, frequency $2n$& wavelength $\lambda/2$
  2. amplitude $A/2$, frequency $2n$& wavelength $\lambda$
  3. amplitude $A$, frequency $2n$& wavelength $2\lambda$
  4. amplitude $A$, frequency $n$& wavelength $\lambda$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using cos^2(theta) = (1 + cos(2*theta))/2, the equation becomes y = A/2 + (A/2)cos(4*pi*n*t - 4*pi*x/lambda). This corresponds to amplitude A/2, frequency 2n, and wavelength lambda/2.