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

The phase difference between two waves represented by 
${y _1} = {10^{ - 6}}\sin \left[ {100t + \frac{x}{{50}} + 0.5} \right]m$
${y _2} = {10^{ - 6}}\cos \left[ {100t + \frac{x}{{50}}} \right]m$
where x is expressed in metres and t is expressed in seconds is approximately

  1. 1.07 rad

  2. 2.07 rad

  3. 0.5 rad

  4. 1.5 rad
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$y _{1}=10^{-6} \sin \left[100 t + \dfrac{x}{50}+ 0.5\right] m$
$y _{2}=10^{-6} \cos \left[100 t + \dfrac{x}{50}\right] m$
So,$y^{1}=10^{-6} \cos\left[\dfrac{\pi}{2}-\left(100 t + \dfrac{x}{50}+0.5\right)\right]$
$y^{1}=10^{-6} \cos \left[\dfrac{-\pi}{2}+100 t+\dfrac{x}{50}+0.5\right]$
$\triangle \phi =\phi _{2}-\phi _{1}$
$\phi _{2}=0$ where as $\phi _{1}=0.5-\dfrac{\pi}{2}$
So,
$\triangle \phi=\phi _{2}-\phi _{1}=\dfrac{\pi}{2}-0.5=1.07 \ rad$
option $-A$ is correct.

































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

Two waves of the same amplitude and frequency arrive at a point simultaneously. what should the phase difference between the waves so that amplitude of the resultant wave is double(2A) 

  1. $\dfrac {\pi}{2} radian$
  2. $\dfrac {2\pi}{3} radian$
  3. $\dfrac {3\pi}{4} radian$

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

Resultant amplitude A_res = sqrt(A1^2 + A2^2 + 2 * A1 * A2 * cos(phi)). For A1 = A2 = A, A_res = 2 * A * cos(phi / 2). For A_res = 2 * A, cos(phi / 2) = 1, so phi / 2 = 0, which means phi = 0.

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

A travelling wave has a velocity of 400 m/s and has a wavelength of 0.5 m. What is the phase difference between two points in the wave that are 1.25 milli secs apart

  1. $2 \pi$
  2. $2 \pi/3$
  3. $2 \pi/5$
  4. $ \pi/6$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The frequency of the wave is $f = v/\lambda=400/0.5=800 Hz$

Time period = 1/800 = 1.25 ms

Thus, both the points are one time period apart. Hence their phase difference will be zero or $2 \pi$

The correct option is (a)

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

Two waves of frequencies 20 Hz and 30 Hz travels out from a common point. The phase difference between them after 0.6 sec is

  1. $12\pi $
  2. ${\pi \over 2}$
  3. $\pi $
  4. ${{3\pi } \over 4}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Beats period$=\cfrac{1}{30-20}=0.1second\ \Delta Y=\cfrac{2\pi}{T}\Delta t\ \quad=\cfrac{2\pi}{0.1}\times0.6=2\pi\times6=12\pi\ \therefore\Delta Y=12\pi$

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

A progressive wave of wavelength 5 cm moves along +X axis. What is the phase difference between two points on the wave separated by a distance of 3 cm at any instant

  1. $3 \pi/5$
  2. $6 \pi/5$
  3. $2 \pi/5$
  4. $7 \pi/5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Phase difference = $(2\pi/5)$ path difference $\implies$ phase difference = $6 \pi/5$

The correct option is (b) 

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

The phase difference between two waves, represented by ${ y } _{ 1 }={ 10 }^{ -6 }\sin { \left[ 100t+\left( x/50 \right) +0.5 \right]\ m } $ and ${ y } _{ 2 }={ 10 }^{ -6 }\cos { \left[ 100t+\left( x/50 \right)  \right]\ m } $. Where $x$ is expressed in metre and $t$ is expressed in seconds, is approximately

  1. $1.07\ radian$
  2. $2.07\ radian$
  3. $0.5\ radian$
  4. $1.5\ radian$
Reveal answer Fill a bubble to check yourself
A Correct answer