Question

15.49 - 30 seconds of exposure to 115 dB sound can damage your hearing, but a much quieter 94 dB may begin to cause damage after 1 hour of continuous exposure. You are going to an outdoor concert, and you'll be standing near a speaker that emits 47 W of acoustic power as a spherical wave. What minimum distance should you be from the speaker to keep the sound intensity level below 94 dB? Express your answer to two significant figures and include the appropriate units.

B. The motion detector used in a physics lab sends and receives 45 kHz ultrasonic pulses. A pulse goes out, reflects off the object being measured, and returns to the detector. The lab temperature is 20 ∘C.. What is the wavelength of the waves emitted by the motion detector? Express your answer in millimeters. How long does it take for a pulse that reflects off an object 3.0 m away to make a round trip? Express your answer in milliseconds.

Answer 1

A)

We use the equation I = P/4*pi*r^2 ……………(a)

I = Intensity in W/m^2

P = power in W

r = radius in m

So the key is converting 94 dB into W/m^2 and by using a conversion online 94 dB is 0.0025 W/m^2 which is our Intensity.

Now we use our Intensity, I = 0.0025 W/m^2 and our given Power P = 47W and putting these numbers into the equation (a) given earlier.

We can rearrange the equation to get r.

0.0025 = (47/4)*pi*r^2

r^2 = 6.773*10^-5

r = 8.23*10^-3 m

r = 8.23 mm

B)

Velocity of a wave in air = 343 m/s

Total meters traveled = 3*2 = 6 m = the wavelength of the waves

Time it takes to travel 6 meters = X s

Now, velocity(v)*time(t) = λ(wavelength) =====> v*t = λ

(343 m/s)(X s) = 6 m

(X s) = (6 m)/(343 m/s)

X = 0.01749 or 17.5 milliseconds to travel 6 m