Two sound sources driven in phase by the same amplifier are 2.10 m apart on the

Question

Two sound sources driven in phase by the same amplifier are 2.10 m apart on the y axis. At a point very far from the y axis, constructive interference is first heard at an angle of 0.146 rad with respect to the x axis and is next heard at 0.295 rad with respect to the x axis. What is the wavelength of the sound waves from the sources?

What is the frequency of the sources? [Use v=340 m/s in air.]

At what angle (in radians) is the next constructive interference heard?

At what angle (in radians) is the first destructive interference heard?

Explanation / Answer

here
d = 2.10 m
A1 = 0.146 rad = 8.365 degrees
A2 = 0.295 rad = 16.902 degrees

Wavelength = W1 = SinA1 * d = sin8.365 * 2
W1 = 0.300 m

similarly,

Wavelength = W2 = SinA2 * d = sin16.902 * 2
W2 = 0.581 m

A)
Frequency = speed of sound in air / wavelength
F1 = 340 / 0.300
F1 = 1133.33 HZ

F2 = 340 / 0.581
F2 = 585.19 Hz

B)
Next contructive interference can be found out by using :

del = m.W1
sinB = m.W1 /d ------------------(1)

using m = 2

For first source:
sinB1 = 0.300 * 2 / 2 = 0.3
B1 = arcSin(0.3)
B1 = 17.45 degrees
B1= 0.305 rad

For Second source:
sinB2 = 0.581 * 2 / 2 = 0.581
B2 = arcSin(0.3)
B2 = 35.52 degrees
B2 = 0.619 rad

C)
First Destructive interference is :

sinB1 = (2m+1)/2 * W1
m =1
sinB1 = 1.5 * W1 -----------------(2)

For first source:
sinB1 = 1.5 * 0.3 = 0.45
B1 = arcSin(0.45)
B1 = 26.74 degrees
B1 = 0.466 rad

For Second source:
sinB1 = 1.5 * 0.581 = 0.871
B2 = arcSin(0.871)
B2 = 60.57 degrees
B2 = 1.057 rad

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.