Chapter 16 - Waves & Sound Flashcards
A microphone is attached to a spring that is
suspended from the ceiling, as shown in
figure. Directly below on the floor is a
stationary 440-Hz source of sound. The
microphone vibrates up and down in simple
harmonic motion with a period of 2.0 s. The
difference between the maximum and
minimum sound frequencies detected by the
microphone is 2.1 Hz. Speed of sound is 343 m/s. Find the amplitude of simple harmonic motion
Not too bad either!!
So you got the formula for doppler effect
fL = (v+vL/v+vS)fs
Now the velocity of the source is 0 since it’s stationary, and since you’re given the max and min frequencies, you have to find that. So when the listener moves toward the source, the velocity is increasing since the frequency increases and when the listener moves away from the source, the velocity decreases since the frequency decreases.
So you’ve got
fs(v+vL/v) - fs (v - vL/v)
(max) - (min)
factor out the fs/v and then you’ve got 2vL
so
deltaF = fs*2vL/V
and rearranging and subbing you should get 0.8185
Find angualr velocity using the f = w/2pi and then find the amplitude using v = aw
Doppler effect signs:
Sign of VL when lsitener moves toward source and away from source
Sign of Vs when source moves toward listener and away from listener
VL
pos (listener toward source)
neg (listener away from source)
Vs
pos (source away from listener)
neg (source toward listener)
A source emits sound uniformly in all directions. A radial
line is drawn from this source. On this line, determine the position
r1 of point 1, which is 1.00 m apart from point 2, such that the
intensity level at one point is 4.00 dB greater than that at the other.
Really not that bad!! :)
So sound intensity is usually L1 - L2 becuase it’s higher intensity - lower
ΔL=10log (I1/I2) (subtraction of logs means division)
And since I is inversely proportional to r then we can sub in r2^2/r1^2
ΔL=10log (r2^2/r1^2)
r2 = r1 + 1
4 = 10log((r1 + 1)^2)/(r1^2)
Divide both sides by ten, bring everything up to the power of 10
10^0.4 = (r1 + 1)^2/r1^2
Sqrt of both sides
1.5849 = r1 + 1/r1
Simplify and solve and you get 1.71m
Transverse vs longitudinal wave
Transverse - disturbance occur perpendicular to wave travel (guitar string)
Longitudinal - disturbance of particles moves same direction as the wave (stretching and compressing) (sound wave)
Outline the inverse square law
I is inversely proportional to 1/r^2
I1/I2 = (r2/r1)^2
As distance from source increases, sound itensity decreases