Interference of Waves

Interactive Feed

A travelling wave represented by $y = A sin (ω t - k x)$ is superimposed on another wave represented by $y = A sin (ω t + k x)$ . The resultant is

a standing wave having nodes at

x = (n + \frac{1}{2}) \frac{λ}{2}, n = 0, 1, 2

a wave travelling along

+ x

a wave travelling along

- x

a standing wave having nodes at

x = \frac{nλ}{2}; n = 0, 1, 2

A tuning fork arrangement (pair) produces 4 beats per second with one fork of frequency 288 cps. A little wax is placed on the unknown fork and then it produces 2 beats per second. The frequency of the unknown fork is

When two tuning forks (fork 1 and fork 2) are sounded simultaneously, 4 beats per second are heard. Now, some tape is attached on the prong of the fork 2. When the tuning forks are sounded again, 6 beats per second are heard. If the frequency of fork 1 is 200 Hz, then what will be the original frequency of fork 2?

Three sound waves of equal amplitudes have frequencies $(ν - 1)$ , $ν$ , $(ν + 1)$ . They superpose to give beat. The number of beats produced per second will be

A tuning fork of known frequency 256 Hz makes 5 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was

(256 + 2)

(256 - 2)

(256 - 5)

(256 + 5)

A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340 Hz. When fork A is filled, the beat frequency decreases to 2 beats/s. What is the frequency of fork A?

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

0.2 I_{0}

I_{0}

3 I_{0}

5.8 I_{0}

The correct figure that shows schematically, the wave pattern produced by superposition of two waves of frequencies 9 Hz and 11 Hz, is

JEE Advanced 2001

Two beams of light having intensities $I$ and $4 I$ interfere to produce a fringe pattern on a screen. The phase difference between the beams is $\frac{π}{2}$ at point $A$ and $π$ at point $B$ . Then the difference between resultant intensities at $A$ and $B$ is

2 I

4 I

5 I

7 I

JEE Advanced 1992

The displacement $y$ of a particle executing periodic motion is given by $y = 4 cos^{2} (\frac{1}{2} t) sin (1000 t)$ . This expression may be considered to be a result of the superposition of ........................ independent harmonic motions.

JEE Advanced 1993

LEVELJEE Advanced

Two radio stations broadcast their programmes at the same amplitude $A$ and at slightly different frequencies $ω_{1}$ and $ω_{2}$ respectively, where $ω_{1} - ω_{2} = 1 0^{3} Hz$ . A detector receives the signals from the two stations simultaneously. It can only detect signals of intensity $\geq 2 A^{2}$ . (a) Find the time interval between successive maxima of the intensity of the signal received by the detector. (b) Find the time for which the detector remains idle in each cycle of the intensity of the signal.

JEE Advanced 2010

When two progressive waves $y_{1} = 4 sin (2 x - 6 t)$ and $y_{2} = 3 sin (2 x - 6 t - \frac{π}{2})$ are superimposed, the amplitude of the resultant wave is

JEE Advanced 1987

LEVELJEE Advanced

The following equations represent transverse waves: $z_{1} = A cos (k x - ω t)$ $z_{2} = A cos (k x + ω t)$ $z_{3} = A cos (k y - ω t)$ Identify the combination(s) of the waves which will produce: (a) standing wave(s), (b) a wave travelling in the direction making an angle of $4 5^{\circ}$ with the positive $X$ and positive $Y$ -axes. In each case, find the position at which the resultant intensity is always zero.

JEE Advanced 2015

Four harmonic waves of equal frequencies and equal intensities $I_{0}$ have phase angles $0$ , $\frac{π}{3}$ , $\frac{2 π}{3}$ and $π$ . When they are superposed, the intensity of the resulting wave is $n I_{0}$ . The value of $n$ is

JEE Advanced 2001

Two pulses in a stretched string, whose centres are initially $8 cm$ apart, are moving towards each other as shown in the figure. The speed of each pulse is $2 cm/s$ . After $2 s$ the total energy of the pulses will be

purely potential

partly kinetic and partly potential

LEVELJEE Advanced

List-I shows four configurations made of straight and semi-circular narrow tubes containing air. A sound wave of wavelength $λ = 0.29 m$ enters these structures at the point $S$ and a sound detector is placed at $D$ . Between the points $S$ and $D$ , the sound travels only through the tubes. List-II contains the possible smallest values of $l$ (refer to the figures) for which the detector $D$ records maximum amplitude. Ignore effects of sharp corners. [Given $cos (1 5^{\circ}) = 0.97$ ]

List-I

List-II

Two coherent sources of sound $S_{1}$ and $S_{2}$ , produce sound waves of the same wavelength $λ = 1 m$ , in phase. $S_{1}$ and $S_{2}$ are placed 1.5 m apart (see figure). A listener, located at $L$ , directly in front of $S_{2}$ finds that the intensity is at a minimum when he is 2 m away from $S_{2}$ . The listener moves away from $S_{1}$ , keeping his distance from $S_{2}$ fixed. The adjacent maximum of intensity is observed when the listener is at a distance $d$ from $S_{1}$ . Then, $d$ is