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
- The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is \( \frac{5}{x} \). The value of \( x \) is ________.
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Two loudspeakers (\(L_1\) and \(L_2\)) are placed with a separation of \(10 \, \text{m}\), as shown in the figure. Both speakers are fed with an audio input signal of the same frequency with constant volume. A voice recorder, initially at point \(A\), at equidistance to both loudspeakers, is moved by \(25 \, \text{m}\) along the line \(AB\) while monitoring the audio signal. The measured signal was found to undergo \(10\) cycles of minima and maxima during the movement. The frequency of the input signal is _____________ Hz.
(Speed of sound in air is \(324 \, \text{m/s}\) and \( \sqrt{5} = 2.23 \))
- The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 cm/s. The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be _________ cm/s.
- 5th harmonic of a closed organ pipe matches with 1st harmonic of an open organ pipe. Find ratio of their lengths.
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Given below are two statements:
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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