PHYSICS

1. Topic 1d
Standing wave and resonance
Formation and characteristics of standing wave
Resonance phenomenon
Natural frequency and resonance frequency
Water goblet resonance
https://www.physicsclassroom.com/class/sound/Lesson-
4/Natural-Frequency

2. Standing wave
• Standing waves are produced whenever two waves of
identical frequency interfere with one another while
traveling opposite directions along the same medium.
• Standing wave patterns are characterized by certain
fixed points along the medium which undergo no
displacement. These points of no displacement are
called nodes, N. (nodes can be remembered as points
of no desplacement).
• Midway between every consecutive nodal point are
points which undergo maximum displacement. These
points are called antinodes; the anti-nodal nodal
positions are labeled by an AN.

3. Natural frequency and resonance
• The frequency or frequencies at which an object tends to vibrate with
when hit, struck, plucked, strummed or somehow disturbed is known
as the natural frequency of the object.
• When an object is subjected to a forced frequency equal to the
natural frequency, the object vibrates with a maximum amplitude.
This phenomenon is known as resonance.

4. Fundamental frequency and harmonics
• The lowest possible frequency at
which a string could vibrate to
form a standing wave pattern is
known as the fundamental
frequency or the first harmonic.
• A harmonic is a wave with a
frequency that is a positive
integer multiple of the frequency
of the original wave, known as
the fundamental frequency.

5. Finding the f of a wave: f=v/
f1 = v/1
= v/4l
f3 = v/3
= 3 v/4l
= 3f1
f5 = v/5
= 5 v/4l
= 5f1
1. Are the wavelengths of each of the harmonics the same?
2. Which wavelength is the longest?
3. When the wavelength is longest, what can we say about its frequency?
4. What is the same about the closed pipe and the wave for the three
pipes above?
5. What is different about the e wave for the three pipes above?

6. Find the frequency of the fundamental and harmonics for the
open pipe.

7. Finding the fundamental frequency of a wire in tension.
The velocity of a traveling wave in a stretched string
is determined by the tension and the mass per unit
length of the string.
 = m/v
m = v
=  AL
 = density of wire
m = mass of wire
A = cross sectional
area of wire
L = length of wire
T = tension of wire
Relation between fundamental frequency
and tension in the wire
https://www.youtube.com/watch?v=BSb-
AQpd7EU

8. The frequency of a standing wave on a string
f = n/2L T/
Find out the what f, n, L, T and  stand for and their units.