PHYSICS 231 Lecture 38: Resonances, beats and review

1
PHYSICS 231Lecture 38 Resonances, beats and
review

• Remco Zegers
• Question hours Thursday 1200-1300
  1715-1815
• Helproom

2
standing waves in a rope
both ends fixed ?n2L/n or Ln?n/2
F tension in rope ? mass per unit length
f1 fundamental frequency
3
Both ends open
4
One end open, one end closed
even harmonics are missing!!!
5
example
A simple flute is played by blowing air in on one
side and the other end is open. The length of the
tube can be varied manually (like a trombone).
What are the frequencies of the first two
possible harmonics if L0.5m? If the length is
made half of the original length, how will these
change v343m/s?
6
example
A simple flute is played by blowing air in on one
side and the other end is closed. The length of
the tube can be varied manually (like a
trombone). What are the frequencies of the first
two possible harmonics if L0.5m? If the length
is made half of the original length, how will
these change v343m/s?
7
harmonics
Generally speaking, many harmonics with different
intensities can be present at the same time.

L
8
beats
Superposition of 2 waves with slightly different
frequency
DEMO
The amplitude changes as a function of time, so
the intensity of sound changes as a function of
time. The beat frequency (number of intensity
maxima/minima per second) fbeatfa-fb
9
example
Someone is trying to tune a guitar. One of the
strings is supposed to have a frequency of 500
Hz. The person is using a tuning fork which
produces a sound of exactly this frequency, but
while sounding the fork and the playing the
guitar, hears a beat in the sound with a
frequency of 3 Hz (3 beat per second). a) What is
the real frequency of the guitar string? b) By
what fraction does the person need to change the
tension of the guitar string to tune it properly?
10
Resonances
Realistically, oscillations are damped due to
frictional forces. However, we can drive the
oscillation via an external source. Example mass
on a spring natural frequency f1/(2?)?(k/m)
If the frequency of the driving force equals the
natural frequency large oscillations occur
Resonance
demo

• Resonances occur in many daily situations
• shock absorber in car
• playing basketball
• resonating lecture room!!

Famous example Tacoma bridge
11
Review
Start with the sample problems on the web to see
how you stand on each chapter!!
see also recitations on Thursday (12-1 and
1715-1815) review on Friday any more???
today one problem each from ch.
2,3,4,5,6 Friday one problem each from 7,8,9 and
the rest 10,11,12,13,14 (2 each)
12
chapter 2.
x(t)x(0)v(0)t½at2 v(t)v(0)at
A person throws 2 stones from the top of a
building with a speed of 20 m/s. One is thrown
up, and the other is thrown down. The first one
hits the street after 5 s. How much later does
the second one hit?
13
chapter 3
v0
A car is trying to jump over a 30m-wide river
using a ramp of 3 m high set at an angle of
300 with the horizontal. a) What is the minimum
velocity v0 required to cross the bridge? b)
What is the highest point of the car?
3m
30m
?300
14
chapter 4
A person is pushing an ice-sledge of 50kg over a
frozen lake with a force of 100N to the east. A
strong wind is pushing from the south-west and
produces a force of20N on the sledge. a) What is
the acceleration of the sledge? b) if the
coefficient of kinetic friction is 0.05, what is
the acceleration?
15
chapter 5
A crate of 50kg is starting to slide from a
slope. When it reaches the bottom, it is caught
by a spring with a spring constant of 1000 N/m.
a) If the crate was originally at a height of 10
m and friction can be ignored, how much is the
spring maximally compressed? b) if the
frictional force is 100N and the length of the
slope is 15m, what is the maximal compression?
16
chapter 6

• Two objects collide head on. Object 1 (m5kg) has
  an
• initial velocity of 10m/s and object 2 (m10 kg)
  has an initial
• velocity of -8 m/s. What is the resulting
  velocity
• of the combined object if the collision is fully
  inelastic?
• of each of the objects if the collision if fully
  elastic?