Interference in Sound Waves

Q.

Two coherent sources of sound, $S_1$ and $S_2$, produce sound waves of the same wavelength, $\lambda =1m$, in phase. $S_1$and $S_2$ are placed $1.5m$ apart (see fig). A listener, located at $L$, directly in front of $S_2$finds that the intensity is at a minimum when he is $2m$ 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 :

1. $12m$

2. $2m$

3. $3m$

4. $5m$

Q.

Two sources of sound, $S_1$ and $S_2$, emitting waves of equal wavelength $20.0cm$, are placed with a separation of $20.0cm$ between them. A detector can be moved on a line parallel to $S_1{S}_2$ and at a distance of $20.0cm$ from it. Initially, the detector is equidistant from the two sources. Assuming that the waves emitted by the sources are in phase, find the minimum distance through which the detector should be shifted to detect a minimum of sound.

Q. Two sound waves having a phase difference of }60^° have path difference of 1)λ/6 2)λ/3 3)2λ 4)λ/2

Q. Two coherent sources $S_1$ and $S_2$ which emit sound of wavelength $\lambda$ in phase are separated by $2\lambda$. A circular wire of large radius is placed in such a way that $S_1{S}_2$ lies in its plane and the middle point of $S_1{S}_2$ is at the centre of the wire as shown below. Find the angular position $\theta$ (in first quadrant) on the wire for which destructive interference takes place.
[Assume the radius of ring $R>>2\lambda$]

1. ${\cos }^{-1}\left(\frac{1}{4}\right)$
2. ${\cos }^{-1}\left(\frac{3}{4}\right)$
3. ${\cos }^{-1}\left(\frac{9}{4}\right)$
4. ${\cos }^{-1}\left(\frac{11}{4}\right)$

Q.

Due to a point isotropic sound source, the sound level at a point is observed as $40dB$. The density of air is $\rho$ = $\frac{15}{11}kg/m^3$ and velocity of sound in air is $330m/s$. (The threshold intensity is ${10}^{-12}\frac{W}{m^2}$)

The pressure amplitude at the observation point is $x\left({10}^{-3}\right)N/m^2$. Then $x$ = _____

1. 3

2. 9

3. 6

4. 2

Q. Two speakers $S_1\text{and}{S}_2$ are derived from the same amplifier and placed at the same distance from $x$-axis as shown in figure. The speakers vibrate in phase at $680\text{Hz}$. A man stands at a point on the $x$-axis at a very large distance from the origin and starts moving parallel to the $y$-axis. The speed of sound is $340\text{m/s}$. Then, at what angle $\theta$ with the $x-$ axis will the intensity of sound drop to a minimum for the first time?

1. ${5.4}^{\circ }$
2. ${9.3}^{\circ }$
3. ${7.2}^{\circ }$
4. ${3.6}^{\circ }$

Q. Two speakers are separated by a distance of $3\text{m}$. A person stands at a distance of $4\text{m}$, directly in front of one of the speakers. If $n$ stands for any integer, find the frequencies (in audible range) for which the listener will hear a minimum sound intensity. Speed of sound in air is $320\text{m/s}$.

1. $200(2n+1)\text{Hz}$
2. $160(2n+1)\text{Hz}$
3. $320(2n+1)\text{Hz}$
4. $80(2n+1)\text{Hz}$

Q. In a Quincke's tube experiment, when the sliding tube is pulled out by $17\text{mm}$, the intensity of sound varies from minimum to maximum value. Find the frequency of sound source, if the speed of sound in air is $340\text{m/s}$.

1. $1\text{kHz}$
2. $2\text{kHz}$
3. $5\text{kHz}$
4. $10\text{kHz}$

Q.

A source $ S$and a detector $ D$ are placed at a distance $ d$ apart. A big cardboard is placed at a distance $ \surd 2d$ from the source and the detector as shown in figure (below). The source emits a wave of wavelength $ d/2$ which is received by the detector after reflection from the cardboard. It is found to be in phase with the direct wave received from the source. By what minimum distance should the cardboard be shifted away so that the reflected wave becomes out of phase with the direct wave?

o D 

Q. A source emitting sound of frequency $90\text{Hz}$ is placed in front of a wall at a distance $3\text{m}$ from it. A detector is also placed in front of the wall at the same distance from it as shown in the figure. Find the minimum distance between the source and the detector for which the detector detects a maximum of sound. Speed of sound in air = $360{\text{ms}}^{-1}$.

1. $2\text{m}$
2. $4\text{m}$
3. $6\text{m}$
4. $8\text{m}$

Q. Sound of wavelength $\lambda$ passes through a Quincke's tube, which is adjusted to give a maximum intensity $I_o.$ The two interfering waves have equal Intensities. Find the minimum distance the sliding tube should be moved to give an intensity $\frac{I_o}{2}.$

1. $\frac{\lambda }{8}$
2. $\frac{\lambda }{2}$
3. $\frac{\lambda }{4}$
4. $\frac{3\lambda }{2}$