A source emits sound uniformly in all directions. There are no reflections of th

Question

A source emits sound uniformly in all directions. There are no reflections of the sound. At a distance r1 from the source the sound is 4.8 dB louder than it is at a distance r2 from the source. What is the ratio r1/r2?

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A transverse wave is traveling on a string. The displacement y of a particle from its equilibrium position is given by y = (0.021 m) sin(25t - 2.0x). Note that the phase angle 25t - 2.0x is in radians, t is in seconds, and x is in meters. The linear density of the string is 1.4 × 10-2 kg/m. What is the tension in the string?

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A long slender bar is made from an unknown material. The length of the bar is 0.739 m, its cross-sectional area is 1.92 × 10-4 m2, and its mass is 2.53 kg. A sound wave travels from one end of the bar to the other end in 2.57 × 10-4 s. Find the Young's modulus of the unknown material.

Explanation / Answer

Question 1) loudness level is given by formula

Loudness level = 10*log(I/I0)

Given , at distance r1 sound is 4.8dB louder than r2

So,

10*log(I1/I0)- 10*log(I2/I0) = 4.8

log(I1/I0)-log(I2/I0) = 0.48

log(I1/I2)=0.48

I1/I2 = 10^.48 = 3.02

Relation between intensity and distance is

Intensity is inversely proportional to square of distance

I1/I2=r2^2/r1^2

3.02 = r2^2/r1^2

r1^2/r2^2 = 1/3.02 = 0.33

r1/r2 = 0.575

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