Interference in Sound Waves

Q.

A person has a hearing range from 20 Hz to 20 kHz. What are the typical wavelengths of sound waves in air corresponding to these two frequencies? Take the speed of sound in air as 344 m/s.

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. $\frac{3\lambda }{2}$

Q. An oscillator of frequency $680\text{Hz}$ drives two speakers. The speakers are fixed on a vertical pole at a distance $3\text{m}$ from each other as shown in figure. A person whose height is almost the same as that of the lower speaker walks towards the lower speaker in a direction perpendicular to the pole. Assuming that there is no reflection of sound from the ground and sound speed is $v=340\text{m/s}$, choose the correct option(s):

1. The person hears the first minimum sound intensity at $18\text{m}$ away from the pole.
2. The person hears the second minimum intensity at a distance of $5.6\text{m}$ from the speaker.
3. The person hears a minimum sound intensity for a total of $6$ times.
4. The person hears a maximum sound intensity for a total of $8$ times.

Q. Two sound sources $S_1$ and $S_2$ emit pure sinusoidal waves in phase. If the speed of sound is $330\text{m/s}$, then for what frequencies does constructive interference occur at P?

1. $500\text{Hz}$
2. $1000\text{Hz}$
3. $1200\text{Hz}$
4. $1500\text{Hz}$

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, the sound detected is changed from a maximum to minimum when sliding tube is moved through a distance $2\text{cm}$. Find the frequency of sound emitted by the source, if the speed of sound in air is $340\text{m/s}$.

1. $2428\text{Hz}$
2. $2125\text{Hz}$
3. $4250\text{Hz}$
4. $8500\text{Hz}$

Q. In Quincke's experiment, the sliding tube is pulled out by such a distance that sound intensity is changed from minimum to maximum. Find the ratio of the amplitudes of the two waves arriving at the detector, if maximum intensity is 16 times that of the minimum intensity.

1. 1 : 2
2. 2 : 1
3. 4 : 5
4. 5 : 3

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 stereo speakers are separated by a distance of 2.40 m. A person stands at a distance of 3.20 m directly in front of the speakers as shown in figure. find the frequencies in the audible range (20-2000 Hz) for which the listener will hear a minimum sound intensity. Speed of sound in air = $320\frac{m}{s}$.

1. $200(2n+1)$

   where $n=0,1,2,......49$

2. $200(2n+1)$

   where $n=0,1,2,......49$

3. $320(2n+1)$

   where $n=0,1,2,......49$

4. $320(2n+1)$

   where $n=0,1,2,......49$

Q. Two sound sources $S_1$ and $S_2$ emit pure sinusoidal waves in phase. If the speed of sound is $330\text{m/s}$, then for what frequencies does constructive interference occur at P?

1. $500\text{Hz}$
2. $1000\text{Hz}$
3. $1200\text{Hz}$
4. $1500\text{Hz}$

Q. Two sinusoidal sound waves were generated from same source after a time gap of 2 sec what is the phase difference between them if their time period is 10s.

1. $\pi$

2. $\frac{\pi }{2}$

3. $\sqrt{3}\frac{\pi }{2}$

4. $\frac{2\pi }{5}$

Q. A sound consists of four frequencies : $200\text{Hz},400\text{Hz},1125\text{Hz}$ and $1600\text{Hz}$. A sound filter is made by passing this sound through a bifurcated pipe as shown. The sound wave has to travel a distance $40\text{cm}$ more in the right branch than in the straight pipe. The speed of sound in air is $300\text{m/s}$. which of the given frequencies will almost completely muffle or silence the outlet?

1. $200\text{Hz}$
2. $400\text{Hz}$
3. $1125\text{Hz}$
4. $1600\text{Hz}$

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. Figure shows a tube structure in which a sound signal is sent from one end and is received at the other end. The semicircular part has a radius of $10.0\text{cm}$. The frequency of the sound source can be varied electronically between $1000\text{Hz}$ and $4000\text{Hz}$. Find the approximate frequency(s) at which a maxima of intensity is detected.

[The speed of sound in air = $340{\text{ms}}^{-1}$]

1. $2110\text{Hz}$
2. $2980\text{Hz}$
3. $8940\text{Hz}$
4. $7840\text{Hz}$

Q. In a Quincke's tube experiment, the sound detected is changed from a maximum to minimum when sliding tube is moved through a distance $2\text{cm}$. Find the frequency of sound emitted by the source, if the speed of sound in air is $340\text{m/s}$.

1. $2428\text{Hz}$
2. $2125\text{Hz}$
3. $4250\text{Hz}$
4. $8500\text{Hz}$

Q. In a Quincke's tube experiment, there is no change in sound intensity being detected at an appropriate point, when the slidable tube is drawn out by $x\text{cm}.$ If the speed of sound in air is $340\text{m/s}$ and frequency of this sounding source is $1700\text{Hz}$, then the value of $x$ is

Q.

A source emitting sound of frequency 180 Hz is placed in front of a wall at a distance of 2 m from it. A detector is also placed in front of the wall at the same distance from it. 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 $m{s}^{-1}$

1. 1 m

2. 2 m

3. 3 m

4. 4 m