Test: Progressive Waves - JEE MCQ

Matter waves are a central part of the theory of quantum mechanics, being an example of wave–particle duality. All matter exhibits wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wave.
Matter is made of atoms, and atoms are made protons, neutrons and electrons. These are not macroscopic particles.

Let the waves be
y1 = Asin(wt)
y2 = Asin(wt + φ)
If φ = π the interference is destructive.
Destructive interference occurs when the maxima of two waves are 180 degrees out of phase: a positive displacement of one wave is cancelled exactly by a negative displacement of the other wave. The amplitude of the resulting wave is zero. The dark regions occur whenever the waves destructively interfere.
Hence B is the correct answer.

A longer wavelength on a fluid interface will result in gravity–capillary waves which are influenced by both the effects of surface tension and gravity, as well as by fluid inertia. On the open ocean, much larger ocean surface waves (seas and swells) may result from coalescence of smaller wind-caused ripple-waves.

Speed of sound in air is 343 m/s or we can say approx 300m/s
And speed of light is approx 300,000,000 m/s
Clearly the ratio is 10⁶

Angular frequency is associated with the number of revolutions an object performs in a certain unit of time. In that sense is related to frequency but in terms of how many times it turns a full period of motion in radians units.
The formula of angular frequency is given by:
Angular frequency = 2 π / (period of oscillation)
ω = 2π / T = 2πf
Where we have:
ω: angular frequency
T: period
f: frequency
Hence C is correct.

'Wave' is a common term for a number of different ways in which energy is transferred: In electromagnetic waves, energy is transferred through vibrations of electric and magnetic fields. In sound waves, energy is transferred through vibration of air particles or particles of a solid through which the sound travels.

20 to 20,000 Hz
The SI unit of audio frequency is the hertz (Hz). It is the property of sound that most determines pitch. The generally accepted standard range of audible frequencies for humans is 20 to 20,000 Hz, although the range of frequencies individuals hear is greatly influenced by environmental factors.

Both transverse and longitudinal waves are mechanical waves where they need material medium to propagate. The motion of transverse wave is perpendicular to the direction of the wave motion, and parallel for longitudinal waves.

v_H/v_O = √(M_O/M_H)
=√(32/2)=4:1.