Question

Question 2: Sound

a.) A person holds a rifle horizontally and fires at a target. The bullet has a muzzle speed of 160 m/s, and the person hears the bullet strike the target 0.80 s after firing it. The air temperature is 73°F. What is the distance to the target?

b.) If one sound is 14 dB greater than another sound, what is the ratio of their intensities (greater/smaller)?

c).  The sound intensity levels for a machine shop and a quiet library are 85 dB and 43 dB, respectively. What is the difference between the intensity of the sound in the machine shop and that in the library?

Answer 1

(A)

c air = 20.0457 * sqrt(K)

K is temperature in kelvinn

F = 73

F = 9/5 K - 459.67

73 = 9/5 K - 459.67

K = (73+459.67)/(5/9)

K = 295.93

c air = 20.0457 * sqrt(295.93) = 344.84 m /s

t1 + t2 = 0.8

d / 160 + d / 344.84 = 0.8

(160+344.84)/d = 1/0.8

or d = 403.87 m

(B)

Beta(f) - Beta(i) = 14 dB

Ratio If/Ii = Log^-1[(Beta(f) - Beta(i))/(10)]

= Log^-1[14/10]

= Log^-1 (1.4)

= 25.12

(C)

Here,

as the dB level is given as

dB =10 * log(I1/Io)

I1 = Io * 10^(dB/10)

for the difference in inetensity

difference in inetensity = 1 *10^-12 * (10^(85/10) - 10^(43/10))

difference in inetensity = 3.162 *10^-4 W/m^2