Reflection, Superposition & Interference

A man standing between two parallel cliffs fires a gun. He hear two echos one after $3$ second and the other after $5$ second. The separation between the two cliffs is $1360$ m, the speed of sound is

A person standing between two parallel cliffs fires a gun and hears two echoes, first echo after 1 second and second echo after 3 second. The distance between the two cliffs is (The velocity of sound $= 330$ m/s)

Two sound waves each of wavelength $\lambda$ and same amplitude $A$ interfere at point $Q$. If the path difference is $\frac{\lambda}{4}$, the amplitude of the resultant wave at point $Q$ is $\left[\sin\frac{\pi}{2} = 1, \cos\frac{\pi}{2} = 0\right]$

Two loudspeakers $(L_1$ and $L_2)$ are placed with a separation of 10 m, as shown in figure. Both speakers are fed with an audio input signal of same frequency with constant volume. A voice recorder, initially at point $A$, at equidistant to both loudspeakers, is moved by 25 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 $\sqrt{5} = 2.23$)

A person standing between two parallel cliffs fires a gun and hears two echoes, first echo after 1 second and the second echo after 3 second. The distance between the two cliffs is (Velocity of sound $= 340\text{ m/s}$)

The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, $y_1(x, t) = 4\sin(kx - \omega t)$ and $y_2(x, t) = 2\sin\left(kx - \omega t + \frac{2\pi}{3}\right)$, are:

(Take the angular frequency of initial waves same as $\omega$)

The equations of two waves are given as

$\begin{matrix} y_1 = a\sin(\omega t + \phi_1) \\ y_2 = a\sin(\omega t + \phi_2) \end{matrix}$

If amplitude and time period of resultant wave is same as the individual waves, then $(\phi_1 - \phi_2)$ is

Two sound waves having same amplitude ' $A$ ' and angular frequency ' $\omega$ ' but having a phase difference of $\left(\frac{\pi}{2}\right)^{c}$ are superimposed then the maximum amplitude of the resultant wave is

A transverse wave strike against a wall,

Equation of simple harmonic progressive wave is given by $y = \frac{1}{\sqrt{a}}\sin\omega t \pm \frac{1}{\sqrt{b}}\cos\omega t$ then the resultant amplitude of the wave is $(\cos 90^\circ = 0)$

The displacement equations of two interfering waves are given by

$y_1 = 10\sin\left(\omega t + \frac{\pi}{3}\right)\text{ cm}, y_2 = 5[\sin\omega t + \sqrt{3}\cos\omega t]\text{ cm}$ respectively.

The amplitude of the resultant wave is _______ $\text{cm}$.

Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm. The phase difference between the individual waves is _________ degree.

Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the $\sqrt{3}$ times of amplitude of individual motions. The phase difference between the two motions is ___________ (degree).

Two waves are superimposed whose ratio of intensities is $9 : 1$. The ratio of maximum and minimum intensity is

The equations of two waves are given by:

y1 = 5 sin 2$\pi$(x - vt) cm

y2 = 3 sin 2$\pi$(x $-$ vt + 1.5) cm

These waves are simultaneously passing through a string. The amplitude of the resulting wave is:

Two waves are simultaneously passing through a string and their equations are: y1 = A1 sin k(x $-$ vt), y2 = A2 sin k(x $-$ vt + x0). Given amplitudes A1 = 12 mm and A2 = 5 mm, x0 = 3.5 cm and wave number k = 6.28 cm${}^{-1}$. The amplitude of resulting wave will be ................ mm.

Three harmonic waves having equal frequency $\nu$ and same intensity $I_0$, have phase angles 0, $\frac{\pi}{4}$ and $-\frac{\pi}{4}$ respectively. When they are superimposed the intensity of the resultant wave is close to:

Two coherent sources of sound, S1 and S2, produce sound waves of the same wavelength, $\lambda$ = 1 m, in phase. S1 and S2 are placed 1.5 m apart (see fig). A listener, located at L, directly in front of S2 finds that the intensity is at a minimum

when he is 2 m away from S2. The listener moves away from S1, keeping his distance from S2 fixed. The adjacent maximum of intensity is observed when the listener is at a distance d from S1. Then, d is:

An engine approaches a hill with a constant speed. When it is at a distance of 0.9 km, it blows a whistle whose echo is heard by the driver after 5 seconds. If the speed of sound in air is 330 m/s, then the speed of the engine is:

Two periodic waves of intensities $I$1 and $I$2 pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is

Two waves having equation x1 = $a$sin($\omega$t $-$ kx + $\phi$1), x2 = asin($\omega$t $-$kx + $\phi$2). If in the resultant wave the frequency and amplitude remain equal to amplitude of superimposing waves, the phase difference between them is

Wave has simple harmonic motion whose period is 4 seconds while another wave which also possesses simple harmonic motion has its period 3 second. If both are combined, then the resultant wave will have the period equal to