The equations of two waves given as \(x=acos\ (ωt + δ)\) and \(y=a cos\ (ωt+α)\), Where \(δ=α+\frac \pi 2\), then resultant wave represent:
The equations of two waves given as \(x=acos\ (ωt + δ)\) and \(y=a cos\ (ωt+α)\), Where \(δ=α+\frac \pi 2\), then resultant wave represent:
- a circle (c.w)
- a circle (a.c.w)
- an Ellipse (c.w)
an ellipse (a.c.w)
The Correct Option is B
Solution and Explanation
When two waves are given by:
\(x = a cos\ (ωt + δ)\)
\(y = a cos\ (ωt + α)\)
And it's given that \(δ = α +\frac \pi2\), it means that the phase difference between the two waves is \(\frac \pi2\).
The resultant wave can be represented by the vector sum of these two waves. If the phase difference between them is \(\frac \pi2\), then the resultant will be a circularly polarized wave.
So, the correct answer is (B): a circle (a.c.w)
Top Questions on Waves
- Let \( \lambda_e \), \( \lambda_p \), and \( \lambda_d \) be the wavelengths associated with an electron, a proton, and a deuteron, all moving with the same speed. Then the correct relation between them is:
- A person can hear a sound of frequency
- Which of the following statements are correct?
(i) Velocity of sound waves is greater in solids than liquids.
(ii) Velocity of sound waves in vacuum is 330 m/s.
(iii) Sound waves are longitudinal waves.
(iv) Velocity of sound waves in vacuum is zero. - If a travelling wave is given by \( y(x, t) = 0.5 \sin(70.1x - 10\pi t) \), where \( x \) and \( y \) are in metres, the time \( t \) is in seconds, then the frequency of the wave is
- The path difference between two waves given by the equations \( y_1 = a_1 \sin\left(\omega t - \frac{2\pi x}{\lambda}\right) \) and \( y_2 = a_2 \sin\left(\omega t - \frac{2\pi x}{\lambda} + \phi\right) \) is
Questions Asked in NEET exam
The current passing through the battery in the given circuit, is:
- NEET (UG) - 2025
- Current electricity
A bob of heavy mass \(m\) is suspended by a light string of length \(l\). The bob is given a horizontal velocity \(v_0\) as shown in figure. If the string gets slack at some point P making an angle \( \theta \) from the horizontal, the ratio of the speed \(v\) of the bob at point P to its initial speed \(v_0\) is :
- NEET (UG) - 2025
- Pendulums
- Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 km/h in the direction X to Y. She notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.
- NEET (UG) - 2025
- Relative Velocity
- The intensity of transmitted light when a polaroid sheet, placed between two crossed polaroids at \(22.5^\circ\) from the polarization axis of one of the polaroids (\(I_0\) is the intensity of polarised light after passing through the first polaroid):
- NEET (UG) - 2025
- Polarization
A full wave rectifier circuit with diodes (\(D_1\)) and (\(D_2\)) is shown in the figure. If input supply voltage \(V_{in} = 220 \sin(100 \pi t)\) volt, then at \(t = 15\) msec:
- NEET (UG) - 2025
- Semiconductor Diode
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