You visited us 3 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

The Effect of Path Difference

Two sound spe...

Question

Two sound speakers are driven in phase by an audio amplifier at frequency $600 H z$ . The speed of sound is $340 m / s$ . The speakers are on the $y$ -axis, one at $y = + 1.0 m$ and the other at $y = - 1.0 m$ . A listener begins at $y = 0$ and walks along a line parallel to the $y$ -axis at a very large distance $x$ away. How many maxima can she possibly hear if she keeps walking in the same direction ?

Open in App

Solution

The path difference is $\sqrt{x^{2} + 1} - x$
So, maxima will be at $△ x = 0$ that means on $x - a x i s$ .
and $△ x = 2 λ / 2 = λ = \frac{v}{f} = \frac{340}{600} = 0.56 m$
After that $x$ will be negative So, she will here $2$ maxima.

Suggest Corrections

Similar questions

Q. Two sound speakers are driven in phase by an audio amplifier at frequency

600 H z

. The speed of sound is

340 m / s

. The speakers are on the

y

-axis, one at

y = + 1.0 m

and the other at

y = - 1.0 m

. A listener begins at

y = 0

and walks along a line parallel to the

y

-axis at a very large distance

x

away. At

{\frac{θ}{2}}^{o}

angle she will first hear a maximum (after

0^{\circ}

) sound intensity. Find

θ

Q. Two sound speakers are driven in phase by an audio amplifier at frequency

600 H z

. The speed of sound is

340 m / s

. The speakers are on the

y

-axis, one at

y = + 1.0 m

and the other at

y = - 1.0 m

. A listener begins at

y = 0

and walks along a line parallel to the

y

-axis at a very large distance

x

away. At what angle

θ^{o}

(between the line from the origin to the listener at the x-axis) will she first hear a minimum sound intensity ?

Q. Two speakers S₁ and S₂, driven by the same amplifier, are placed at y = 1.0 m and y = −1.0 m. The speakers vibrate in phase at 600 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 in air is 330 m s⁻¹. (a) At what angle θ will the intensity of sound drop to a minimum for the first time? (b) At what angle will he hear a maximum of sound intensity for the first time? (c) If he continues to walk along the line, how many more can he hear?

Q. Two speakers

S_{1} 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 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 m/s

. Then, at what angle

θ

with the

x -

axis will the intensity of sound drop to a minimum for the first time?

Two audio speakers are kept some distance apart and are driven by the same amplifier system. A person is sitting at a place 6.0 m from one of the speakers and 6'4 m from the other. If the sound signal is continuously varied from 500 Hz to 6000 Hz, what are the frequencies for which there is a destructive interference at the place of the listener? Speed of sound in air = 320 m/s.

Join BYJU'S Learning Program

The path difference is √x2+1−xSo, maxima will be at △x=0 that means on x−axis.and △x=2λ/2=λ=vf=340600=0.56mAfter that x will be negative So, she will here 2 maxima.

The path difference is $\sqrt{x^{2} + 1} - x$
So, maxima will be at $△ x = 0$ that means on $x - a x i s$ .
and $△ x = 2 λ / 2 = λ = \frac{v}{f} = \frac{340}{600} = 0.56 m$
After that $x$ will be negative So, she will here $2$ maxima.