In Fig. 17-46, sound of wavelength is emitted isotropically by point source S. Sound ray 1 extends directly to detector D, at distance . 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 SD line, at distance d from the line. Assume that the reflection shifts the sound wave by . 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 and (b) exactly in phase?
We can find the path difference between the direct and reflected waves. Then using the conditions for constructive and destructive interference, we can find the least value of d, for which the direct and reflected sounds arrive at D exactly in phase and out of phase.
The cosine law for side c of triangle,
The linear expansion formula,
Path difference between direct and reflected wave using equations (i) and (ii) is given as:
For destructive interference, the least value of d is given as:
Hence the value of d is, .
Excluding zero, the least value is found to be .
Therefore, the least value of d for which the direct and reflected sounds arrive at D exactly out of phase is .
For constructive interference, the least value of d is given as:
Solving this, we get the least value of d as:
Therefore, the least value of d for which the direct and reflected sounds arrive at D exactly in phase is .
The speed of sound in a certain metal is . One end of a long pipe of that metal of length L is struck a hard blow. A listener at the other end hears two sounds, one from the wave that travels along the pipe’s metal wall and the other from the wave that travels through the air inside the pipe.
(a) If role="math" localid="1661511418960" is the speed of sound in air, what is the time interval between the arrivals of the two sounds at the listener’s ear?
(b) If and the metal is steel, what is the length ?
Two atmospheric sound sources emit isotropically at constant power. The sound levels of their emissions are plotted in Figure versus the radial distance from the sources . The vertical axis scale is set by and .
What are (a) the ratio of the larger power to the smaller power and
(b) the sound level difference at ?
Question: Hot chocolate effect Tap a metal spoon inside a mug of water and note the frequency fi you hear. Then add a spoonful of powder (say, chocolate mix or instant coffee) and tap again as you stir the powder. The frequency you hear has a lower value fs because the tiny air bubbles released by the powder change the water’s bulk modulus. As the bubbles reach the water surface and disappear, the frequency gradually shifts back to its initial value. During the effect, the bubbles don’t appreciably change the water’s density or volume of dV/dp - that is , the differential change in volume due to the differential change in the pressure caused by the sound wave in the water . If =0.333, what is the ratio?
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