Figure shows an air filled, acoustic interfero meter, used to demonstrate the interference of sound waves. Sound source $$ S $$ is an oscillating diaphragm; $$ D $$ is a sound detector, such as the ear or a microphone. Path $$ S B D $$ can be varied in length, but path $$ S A D $$ is fixed. At $$ D, $$ the sound wave coming along path $$ S B D $$ interferes with that coming along path $$ S A D . $$ In one demonstration, the sound intensity at $$ D $$ has a minimum value of 100 units at one position of the movable arm and continuously climbs to a maximum value of 900 units when that arm is shifted by $$ 1.65 \mathrm{cm} . $$ Find the frequency of the sound emitted by the source.
When the right side of the instrument is pulled out a distance $$ d $$, the path length for sound waves increases by $$ 2 d $$.
since the interference pattern changes from a minimum to the next maximum, this distance must be half a wavelength of the sound.
So $$ 2 d=\lambda / 2 $$ where $$ \lambda $$ is the wavelength.
Thus $$ \lambda=4 d $$ and, if $$ v $$ is the speed of sound, the frequency is
$$f=v /\lambda=v / 4 d=(343 \mathrm{m} / \mathrm{s}) / 4(0.0165 \mathrm{m})=5.2 \times 10^{3} \mathrm{Hz}$$
Two coherent narrow slits emitting sound of wavelength $$\lambda$$ in the same phase are placed parallel to each other at a small separation of $$2\lambda$$. The sound is detected by moving a detector on the screen $$\displaystyle\sum$$ at a distance $$D(>>\lambda)$$ from the slit $$S_{1}$$ as shown in figure. Find the distance $$x$$ such that the intensity at $$P$$ is equal to the intensity at $$O$$.
Figure shows two coherent sources $$S_{1}$$ and $$S_{2}$$ which emit sound of wavelength $$\lambda$$ in phase. The separation between the sources is $$3\lambda$$. A circular wire of large is placed in such a way that $$S_{1}S_{2}$$ lies in its plane and the middle point $$S_{1}S_{2}$$ is at the centre of the wire. Find the angular position $$\theta$$ on the wire for which constructive takes place.
Figure shows two isotopic point sources of sound, $$S_1$$ and $$S_2$$. The sources emit wave in phase at wavelength 0.50 m; they are separated by D = 1.75 m. If we move a sound detector along a large circle centered at the midpoint between the sources, at how many points do waves arrive at the detector (a) exactly in phase and (b) exactly out of phase?
Figure shows four isotopic point sources of sound that are uniformly spaced on an x-axis. The sources emit sound at the same wavelength $$\lambda$$ and same amplitude $$s_m$$, and they emit in phase A point P is shown on the x axis. Assume that as the sound waves travel to P, the decrease in their amplitude is negligible. What multiple of $$s_m$$ is the amplitude of the net wave at P if distance d in the figure is (a) $$\lambda/4$$ (b) $$\lambda/2$$, and (c) $$\lambda$$?
Party hearing. As the number of people at a party increases, you must raise your voice for a listener to hear you against the backgrounds noise of the other partygoers. However, once you reach the level of yelling, the only way you can be heard is if you move closer to your listener, into the listener's "personal space". Model the situation by replacing you with an isotropic point source of fixed power P and replacing your listener with a point that absorbs part of your sound waves. These points are initially separated by $$r_1 = 1.20 \space m$$. If the background noise increases by $$\Delta \beta = 5 \space dB$$, the sound level at your listener must also increase. What separation $$r_f$$ is then required?
In Fig. sound of wavelength $$ 0.850 \mathrm{m} $$ is emitted isotropically by point source $$ S $$. Sound ray 1 extends directly to detector $$ D $$, at distance $$ L=10.0 \mathrm{m} $$. Sound ray 2 extends to $$ D $$ via a reflection (effectively, a "bouncing") of the sound at a flat surface. That reflection occurs on a perpendicular bisector to the $$ S D $$ line, at distance $$ d $$ from the line. Assume that the reflection shifts the sound wave by $$ 0.500 \lambda $$. For what least value of $$ d $$ (other than zero) do the direct sound and the reflected sound arrive at $$ D $$ (a) exactly out of phase?
In Fig. sound of wavelength $$ 0.850 \mathrm{m} $$ is emitted isotropically by point source $$ S $$. Sound ray 1 extends directly to detector $$ D $$, at distance $$ L=10.0 \mathrm{m} $$. Sound ray 2 extends to $$ D $$ via a reflection (effectively, a "bouncing") of the sound at a flat surface. That reflection occurs on a perpendicular bisector to the $$ S D $$ line, at distance $$ d $$ from the line. Assume that the reflection shifts the sound wave by $$ 0.500 \lambda $$. For what least value of $$ d $$ (other than zero) do the direct sound and the reflected sound arrive at $$ D $$ (b) exactly in phase?
Figure shows an air filled, acoustic interfero meter, used to demonstrate the interference of sound waves. Sound source $$ S $$ is an oscillating diaphragm; $$ D $$ is a sound detector, such as the ear or a microphone. Path $$ S B D $$ can be varied in length, but path $$ S A D $$ is fixed. At $$ D, $$ the sound wave coming along path $$ S B D $$ interferes with that coming along path $$ S A D . $$ In one demonstration, the sound intensity at $$ D $$ has a minimum value of 100 units at one position of the movable arm and continuously climbs to a maximum value of 900 units when that arm is shifted by $$ 1.65 \mathrm{cm} . $$ Find the ratio of the amplitude at $$ D $$ of the $$ S A D $$ wave to that of the $$ S B D $$ wave.
Figure $$ 17-48 $$ shows an air filled, acoustic interfero meter, used to demonstrate the interference of sound waves. Sound source $$ S $$ is an oscillating diaphragm; $$ D $$ is a sound detector, such as the ear or a microphone. Path $$ S B D $$ can be varied in length, but path $$ S A D $$ is fixed. At $$ D, $$ the sound wave coming along path $$ S B D $$ interferes with that coming along path $$ S A D . $$ In one demonstration, the sound intensity at $$ D $$ has a minimum value of 100 units at one position of the movable arm and continuously climbs to a maximum value of 900 units when that arm is shifted by $$ 1.65 \mathrm{cm} . $$ Find How can it happen that these waves have different amplitudes, considering that they originate at the same source?