The document explains standing waves, which are formed by two waves moving in opposite directions, creating fixed points called nodes and moving points called anti-nodes. It discusses the relationship between the string length and fundamental frequency, noting that increasing the length decreases the frequency, and provides questions and solutions related to harmonics and resonant frequencies. Visual aids and examples are included to enhance understanding of the concepts presented.

2. WHAT IS A STANDING WAVE?
• The vibration modes associated with strings
, for example, have patterns called standing
waves.
• Standing waves are combinations of two
waves moving in opposite directions to
each other.
• They have particular points that are fixed
(frequency for e.g.), whereas other points
between them vibrate with a maximum
amplitude.

3. NODES & ANTI-NODES
• Nodes: Points on the string that
are rest all the time and have 0
amplitude.
• Anti-nodes: points that move
with the max. amplitude (2A).

4. Q #1: WHICH OPTION CORRESPONDS TO THE
CORRECTLY LABELED NODES AND ANTINODES?
(CHOOSE ALL THAT APPLY)
A. Point A and C are nodes.
B. Point A & B are nodes.
C. Point C & D are nodes.
D.Point A & C are antinodes.
E. Point B & D are antinodes.
F. All are false.
A C
DB

5. Q #1 SOLUTION.
A. Point A and C are nodes.
B. Point A & B are nodes.
C. Point C & D are nodes.
D.Point A & C are antinodes.
E. Point B & D are antinodes.
F. All are false.
A C
DB

6. FUNDAMENTAL FREQUENCY (“FIRST HARMONIC”)
STANDING WAVE
• Has the lowest frequency and
longest wavelength.
• Remember, “T” in this formula
refers to Tension Force not Period!

7. FIRST HARMONIC STANDING WAVE
http://www.chemistry.wustl.edu/~coursedev/Online%20tutorials/waves/fundamental.gif

8. Q#2: TRUE OR FALSE? IF THE LENGTH OF THE
STRING IS INCREASED, THE FUNDAMENTAL
FREQUENCY WILL DECREASE.
A)True
B)False

9. Q#2 SOLUTION.
A) True
B) False
The fundamental frequency does in fact decrease when
the length of the string is increased. This can be seen
from the formula above, assuming if the mass and
string tension are kept the same. If the length is
increased the components in the square root will
decrease while the denominator (2L) will increase
resulting in an overall decrease of frequency.

10. Q#3: WHAT IS THE MASS OF A STRING WITH
LENGTH 2 M, TENSION OF 500 N AND
FUNDAMENTAL OF 10 HZ?
Disclaimer: Question components are not to scale, random
numbers were used for understanding and learning purposes.
A) 0.500 g
B) 0.450 g
C) 0.625g
D) 0.200 g

11. Q#3 SOLUTION.
Disclaimer: Question components are not to scale, random
numbers were used for understanding and learning purposes.
A) 0.500 g
B) 0.450 g
C) 0.625 g
D) 0.200 g

12. WRITTEN SOLUTION EXPLAINED

13. HARMONICS OR RESONANT FREQUENCIES
The allowed frequencies for a standing wave.

14. http://i65.servimg.com/u/f65/15/05/64/90/harmon11.jpg

15. Q#4: IF A STRING HAS A FOURTH
HARMONIC OF 20 HZ WHAT IS THE
FUNDAMENTAL?
A) 20 Hz
B) 10 Hz
C) 15 Hz
D) 30 Hz
E) None of the above.

16. Q#4 SOLUTION.
A) 20 Hz
B) 10 Hz
C) 15 Hz
D) 30 Hz
E) None of the
above.
4th Harmonic= 20
Hz
So fundamental or
1st harmonic=
20 Hz/4= 5Hz

17. THANK
YOU!