Question:
A wave represented by the equation $y_1$ = $a\, cos (kx - \omega \,t$) is superimposed with another wave to form a stationary wave such that the point $x = 0$ is node. The equation for the other wave is
A wave represented by the equation $y_1$ = $a\, cos (kx - \omega \,t$) is superimposed with another wave to form a stationary wave such that the point $x = 0$ is node. The equation for the other wave is
Updated On: Jul 2, 2022
- $a\,cos\left(kx-\omega t+\pi\right)$
- $a\,cos\left(kx+\omega t+\pi\right)$
- $a\,cos\left(kx+\omega t+\frac{\pi}{2}\right)$
- $a\,cos\left(kx-\omega t+\frac{\pi}{2}\right)$
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Since the point x = 0 is a node and reflection is taking place from point x = 0. This means that reflection must be taking place from the fixed end and hence the reflected ray must suffer an additional phase change of $\pi$ or a
path change of $\frac{\lambda}{2}.$
So, if $y_{incident} = a\, COS \left( kx - \omega t \right)$
$\Rightarrow\quad y_{incident} = a \,COS \left(-kx - \omega t + \pi\right)$
$= - a\, cos \left(\omega t + kx\right)$
Hence equation for the other wave
$y = a \,cos\left(kx+\omega t + \pi\right)$
Was this answer helpful?
0
0
Top Questions on Waves
- The displacement of a travelling wave \( y = C \sin \left( \frac{2\pi}{\lambda} (at - x) \right) \), where \( t \) is time, \( x \) is distance and \( \lambda \) is the wavelength, all in S.I. units. Then the frequency of
- A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with fundamental frequency of 600 Hz under same tension _______ cm.
- The equation of a stationary wave is:
\[y = 2a \sin\left(\frac{2\pi nt}{\lambda}\right) \cos\left(\frac{2\pi x}{\lambda}\right)\]Which of the following is NOT correct: - A closed organ pipe 150 cm long gives 7 beats per second with an open organ pipe of length 350 cm, both vibrating in fundamental mode. The velocity of sound is ________ m/s.
- A plane progressive wave is given by \( y = 2 \cos 2\pi(330t - x) \, \text{m} \). The frequency of the wave is:
View More Questions
Questions Asked in AIEEE exam
- This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. It is not possible to make a sphere of capacity $1$ farad using a conducting material. It is possible for earth as its radius is $6.4 \times 10^6\,m$.
- AIEEE - 2012
- electrostatic potential and capacitance
- A steel wire can sustain $100\, kg$ weight without breaking. If the wire is cut into two equal parts, each part can sustain a weight of
- AIEEE - 2012
- mechanical properties of solids
- The limiting line in Balmer series will have a frequency of (Rydberg constant, $R_{\infty}=3.29\times10^{15}$ cycles/s)
- AIEEE - 2012
- Electromagnetic Spectrum
- Which of the plots shown in the figure represents speed (v) of the electron in a hydrogen atom as a function of the principal quantum number (n)?
- The ratio of number of oxygen atoms (O) in 16.0 g ozone $(O_3), \,28.0\, g$ carbon monoxide $(CO)$ and $16.0$ oxygen $(O_2)$ is (Atomic mass: $C = 12,0 = 16$ and Avogadro?? constant $N_A = 6.0 x 10^{23}\, mol^{-1}$)
- AIEEE - 2012
- Mole concept and Molar Masses
View More Questions
Concepts Used:
Waves
Waves are a disturbance through which the energy travels from one point to another. Most acquainted are surface waves that tour on the water, but sound, mild, and the movement of subatomic particles all exhibit wavelike properties. inside the most effective waves, the disturbance oscillates periodically (see periodic movement) with a set frequency and wavelength.
Types of Waves:
Transverse Waves -
Waves in which the medium moves at right angles to the direction of the wave.
Examples of transverse waves:
- Water waves (ripples of gravity waves, not sound through water)
- Light waves
- S-wave earthquake waves
- Stringed instruments
- Torsion wave
The high point of a transverse wave is a crest. The low part is a trough.
Longitudinal Wave -
A longitudinal wave has the movement of the particles in the medium in the same dimension as the direction of movement of the wave.
Examples of longitudinal waves:
- Sound waves
- P-type earthquake waves
- Compression wave