Question

Two loudspeakers sit next to each other on a line in a 10◦C room.They both emit...

Two loudspeakers sit next to each other on a line in a 10◦C room.They both emit a 660 Hz sound

1. If the speakers have the same phase constant, what is the smallest distance between the speakers for which the interference of thesound waves is perfectly constructive?

2. If the speakers have phase constant difference equal to π, what isthe smallest distance between the speakers for which the interference of the sound waves is perfectly constructive?

3. If the speakers have the same phase constant, what is the smallest distance between the speakers for which the interference of the sound waves is perfectly destructive?

Homework Answers

Answer #1

v = λ × f        λ = v / f ..........(A)

Here, V= speed of sound at temperature 10 degree.

Temperature dependence of speed of sound is given by

T is in kelvin.

so, at 10 C, V = 337.51 m/s.

so, Using equation A.

λ(wavelength) = 51.138 cm.

1. If they have the same phase, they will interfere constructively if their high amplitute coincide with each other. this would happen if they are placed atleast half a wave length away.

so, the minimum Distance = 51.138/2 = 25.56 cm. Ans.

2. If they have a phase difference of pi. They need to have a distance of one wavelength between them.

so, Minimum distance = 51.138 cm.

3. Now they have same phase, their low and high would meet once they have a distance of one wavelength.

so, Minimum distance is again 51.138 cm.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Two loudspeakers are in a room where the speed of sound is 343 m/s. They emit...
Two loudspeakers are in a room where the speed of sound is 343 m/s. They emit 531 Hz sound waves along the x-axis. If the speakers are in phase, what is the smallest distance between the speakers for which the interference of the sound waves is perfectly destructive (in m)?
Two loudspeakers emit coherent in phase sound waves with at a frequency of 68.8 Hz. The...
Two loudspeakers emit coherent in phase sound waves with at a frequency of 68.8 Hz. The speed of sound is 344.0 m/s. Point q is vertically located 2.0 m from the bottom speaker and 5.0 m from the top speaker. At point q, is there maximum constructive interference, complete destructive interference, or neither?? Explain your answer.
Two in-phase loudspeakers are 3.0 m apart. They emit sound with a frequency of 950Hz. A...
Two in-phase loudspeakers are 3.0 m apart. They emit sound with a frequency of 950Hz. A microphone is placed half-way between the speakers and then moved along the line joining the two speakers until the first point of destructive interference is found. At what distance from that midpoint is that first point? The speed of sound in air is 343 m/s. A) 0.09 m B) 0.18 m C) 0.24m D) 0.36m E) There is no point in that line where...
Two loudspeakers are placed at either end of a gymnasium, both pointing toward the center of...
Two loudspeakers are placed at either end of a gymnasium, both pointing toward the center of the gym and equidistant from it. The speakers emit 276 Hz sound that is in phase. An observer at the center of the gym experiences constructive interference. Part A How far toward either speaker must the observer walk to first experience destructive interference?
Two loudspeakers emit 500 Hz sound waves with an amplitude of 1cm. Speaker 2 is 1.00m...
Two loudspeakers emit 500 Hz sound waves with an amplitude of 1cm. Speaker 2 is 1.00m behind speaker 1, and the phase difference between the speakers is 90 degree . (I) What is the phase difference of the sound wave at a point 2.00 m in front of speaker 1? (II) What is the minimum distance between the two speakers such that the observer at this position hears the minimal sound? (6 points)
Follow these steps to solve this problem: Two identical loudspeakers, speaker 1 and speaker 2, are...
Follow these steps to solve this problem: Two identical loudspeakers, speaker 1 and speaker 2, are 2.0 m apart and are emitting 1700-Hz sound waves into a room where the speed of sound is 340 m/s. Consider a point 4.0 m in front of speaker 1, which lies along a line from speaker 1, that is perpendicular to a line between the two speakers. Is this a point of maximum constructive interference, a point of perfect destructive interference, or something...
Two loudspeakers that emit sound of 686 Hz, but 900 out of phases are placed along...
Two loudspeakers that emit sound of 686 Hz, but 900 out of phases are placed along walls on the opposite sides of a gym and are separated by a distance of 25.00m. (I)If Janet starts walking from one speaker towards the other speaker, how far does she have to walk before she hears the first constructive interferences? (II) What is the phase difference when she is midway between the two speakers? The speed of sound in air is 343.0m/s.
Two identical loudspeakers are situated at the same height above a horizontal xy-plane and emit sound...
Two identical loudspeakers are situated at the same height above a horizontal xy-plane and emit sound waves of frequency 1660 Hz. The speakers are located at coordinates (0,1.57) and (0,-1.57), with units in meters. A point O on the x-axis a distance x1 = 9.1 meters away (x1,0) is the location of an interference maximum. A second point P at (x1, y2) is the location of the first minimum of sound intensity when moving away from point O in the...
9. Two loudspeakers emit sound waves along the x-axis. The sound has maximum intensity when the...
9. Two loudspeakers emit sound waves along the x-axis. The sound has maximum intensity when the speakers are 20 cm apart. The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 60 cm. (a) What is the wavelength of the sound? (b) If the distance between the speakers continues to increase, at what separation will the sound intensity again be a maximum?
Two loudspeakers emit identical sound waves along the x-axis. The sound at a point on the...
Two loudspeakers emit identical sound waves along the x-axis. The sound at a point on the axis has maximum intensity when the speakers are 25 cm apart. The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 55 cm. A) What is the wavelength of the sound? Express your answer with the appropriate units. B) If the distance between the speakers continues to increase, at what separation will the sound intensity again...