Physics

Wave Motion

489 Questions

Wave motion questions cover the principles of traveling and stationary waves, including their equations and intensities. The topics explore interference patterns, phase differences, and electromagnetic radiation speeds. Mastery of these concepts is vital for physics sections in engineering and civil services examinations.

Wave interferenceStanding wavesPhase differenceElectromagnetic radiationWave equations

Wave Motion Questions

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

Two waves are represented by the equations $y _{1}a sin (\omega t+kx+0.57)m$ $y _{2}a cos (\omega t+kx)m$  
where x in meter and t in Sec.  the phase difference between them is 

  1. 0.57 radian

  2. 1.0 radian

  3. 1.25 radian

  4. 1.57 radian
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Convert y2 to sine form: y2 = a sin(omega*t + kx + pi/2). The phase of y1 is omega*t + kx + 0.57. The phase of y2 is omega*t + kx + 1.57. The difference is 1.57 - 0.57 = 1.0 radian.

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

Two waves have equations ${x} _{1}=a\sin{(\omega t+{\phi} _{1})}$ and ${x} _{2}=a\sin{(\omega t+{\phi} _{2})}$. If in the resultant wave the frequency and amplitude remain equal to amplitude of superimposing waves. The phase difference between them is:

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

The amplitude of the resultant of two waves with equal amplitudes a and phase difference phi is given by A = sqrt(2a^2 + 2a^2 cos(phi)). Setting the resultant amplitude equal to a gives 1 + cos(phi) = -1/2, leading to cos(phi) = -1/2, so phi = 2pi / 3.

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

Consider the wave represented by $y=\cos(500t-70x)$ where $x$ is in metres and $t$ in seconds. the two nearest points in the same phase have a separation of 

  1. $2\pi/7\ m$
  2. $2\pi/7\ cm$
  3. $20\pi/7\ m$
  4. $20\pi/7\ cm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For the same phase, the path difference must be a multiple of the wavelength. Here, k = 70, so 2pi/lambda = 70, lambda = 2pi/70 m = 2pi/70 * 100 cm = 20pi/7 cm.

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

Four waves are expressed as
(i) $y _ { 1 } = a _ { 1 } \sin \omega t$                                            (ii) $y _ { 2 } = a _ { 2 } \sin 2 \omega t$
(iii) $y _ { 3 } = a _ { 3 } \cos \omega t$                                         (iv) $y _ { 4 } = a _ { 4 } \sin ( \omega t + \phi )$
The interference is possible between

  1. (i) and (iii)

  2. (i) and (ii)

  3. (ii) and (iv)

  4. Not possible at all
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
For interference frequency should be same.
Ans. (A)
Multiple choice problems on properties of waves terms and defination used in wave motion oscillation and waves waves physics

If x=$\theta sin(\alpha + \dfrac{\pi}{6})$ and $x^1 = {\theta}cos\alpha$,then what is the phase difference between the two waves.

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

Rewriting x = theta * sin(alpha + pi/6) and x' = theta * cos(alpha) = theta * sin(alpha + pi/2), the phase difference between the two sine waves is the difference in their phase angles, which is (alpha + pi/2) - (alpha + pi/6) = pi/3.

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

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 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.

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

The equation of a wave is given by 
$ Y\quad =\quad A\quad sin\quad \omega \left( \frac { x }{ v } -k \right)  $
Where $ \omega $ is the angular velocity and v is the linear velocity.The dimensions of K is

  1. LT

  2. T
  3. $ T^{-1} $
  4. $ T^2 $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In the argument omega(x/v - k), the dimensions of omega are T^-1. For the argument to be dimensionless, (x/v - k) must have dimensions of T. Since x/v is distance/velocity = time, k must also have dimensions of time.

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

The equation of a progressive wave is $Y= a sin(200 t-x)$, where x is in meter and t is in second. The velocity of wave is

  1. $200 $ m/sec
  2. $100 $ m/sec
  3. $50 $ m/sec

  4. None
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The wave equation is y = a sin(200t - x). The standard form is y = a sin(omega*t - k*x). Here omega = 200 and k = 1. Wave velocity v = omega/k = 200/1 = 200 m/s.

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

The equation of a wave travelling on a stretched string is :
$y=4\sin 2\pi \left(\dfrac{t}{0.02}-\dfrac{x}{100}\right)$
Here $x$ and $y$ are in $cm$ and $t$ is in second. the relative deformation amplitude of medium is :

  1. $0.02\pi$
  2. $0.08\pi$
  3. $0.06\pi$
  4. $none\ of\ these$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The relative deformation (strain) is dy/dx. y = 4 sin(2pi*t/0.02 - 2pi*x/100). dy/dx = 4 * (-2pi/100) * cos(...) = -0.08pi * cos(...). The amplitude of this is 0.08pi.