The source of a sound wave has a power of $$1.00 \mu W$$. If it is a point source, (a) what is the intensity 3.00 m away and (b) what is the sound level in decibels at that distance?
(a) The intensity is a given by $$I = P/4\pi r^{2}$$ when the source is "point-like". Therefore, at $$r= 3.00 \space m$$,
$$I = \frac{1.00 \times 10^{-6} \space W} {4\pi\left (3.00 m \right )^{2}} $$
$$= 8.84 \times 10^{-9} \space W/m^{2}$$.
(b) The sound level there is
$$\beta = 10 \log \left ( \frac{8.84 \times 10^{-9} \space W/m^{2}} {1.00 \times 10^{-12} \space W/m^{2}} \right ) = 39.5 dB$$
The noise level in a classroom in absence of the teacher is $$50\ dB$$ when $$50$$ students are present. Assuming that on the average each student outputs same sound energy per second, what will be the noise level if the number of students is increased to $$100$$?
A 1.0 W point source emits sound waves isotropically. Assuming that the energy of the waves is conserved, find the intensity (a) 1.0 m from the source and (b) 2.5 m from the source.
Approximately a third of with normal hearing have ears that continuously emit a low-intensity sound outward through the ear canal. A person with such spontaneous otoacoustic emission is rarely aware of the sound, except perhaps in a noise-free environment, but occasinally the emission is loud enough to be heard by someone else nearby. In one observation, the sound wave had a frequency of 1665 Hz and a pressure amplitude of $$1.13 \times 10^{-3} Pa$$. What were (a) the displacement amplitude and (b) the intensity os the wave emitted by the ear?
A point source emits $$30.0 \space W$$ of sound isotropically. A small microphone intercepts the sound in an area of $$0.750 \space cm^{2}, 200 \space m$$ from the source. Calculate (a) the sound intensity there and (b) the power intercepted by the microphone.
A certain loudspeaker system emits sound isotropically with a frequency of $$ 2000 \mathrm{Hz} $$ and an intensity of $$ 0.960 \mathrm{mW} / \mathrm{m}^{2} $$ at distance of $$ 6.10 \mathrm{m} $$. Assume that there are no reflections.What is the intensity at $$ 30.0 \mathrm{m} ? $$
Find the ratios (greater to smaller) of the intensities for two sounds whose sound levels differ by 37 dB.
On July $$ 10,1996, $$ a granite block broke away from a wall in Yosemite Valley and, as it began to slide down the wall, was launched into projectile motion. Seismic waves produced by its impact with the ground triggered seismographs as far away as $$ 200 \mathrm{km} . $$ Later measurements indicated that the block had a mass between $$ 7.3 \times 10^{7} \mathrm{kg} $$ and $$ 1.7 \times 10^{8} \mathrm{kg} $$ and that it landed $$ 500 \mathrm{m} $$ vertically below the launch point and $$ 30 \mathrm{m} $$ horizontally from it. (The launch angle is not known.) (a) Estimate the block's kinetic energy just before it landed. Consider two types of seismic waves that spread from the impact point-a hemispherical body wave traveled through the ground in an expanding hemisphere and a cylindrical surface wave traveled along the ground in an expanding shallow vertical cylinder (Fig. $$ 17-49 $$ ). Assume that the impact lasted $$ 0.50 \mathrm{s} $$, the vertical cylinder had a depth $$ d $$ of $$ 5.0 \mathrm{m}, $$ and each wave type received $$ 20 \% $$ of the energy the block had just before impact. Neglecting any mechanical energy loss the waves experienced as they traveled, determine the intensities of (b) the body wave and (c) the surface wave when they reached a seismograph $$ 200 \mathrm{km} $$ away. (d) On the basis of these results, which wave is more easily detected on a distant seismograph?
The sound intensity is $$ 0.0080 \mathrm{W} / \mathrm{m}^{2} $$ at a distance of $$ 10 \mathrm{m} $$ from an isotropic point source of sound. What is the sound intensity $$ 5.0 \mathrm{m} $$ from the source?
The sound intensity is $$ 0.0080 \mathrm{W} / \mathrm{m}^{2} $$ at a distance of $$ 10 \mathrm{m} $$ from an isotropic point source of sound. What is the sound level 10 m from the source?
Suppose a spherical loudspeaker emits sound isotropically at $$ 10 \mathrm{W} $$ into a room with completely absorbent walls, floor, and ceiling (an anechoic chamber). What is the intensity of the sound at distance $$ d=3.0 \mathrm{m} $$ from the center of the source?