Learning Object 2 for standing waves on a string

1. Standing Waves on Strings
Alex Law
36551142
PHYS 101 LF2

2. Standing Waves on Strings
• Interference of two waves that move in the
opposite direction
– Consists of two harmonic waves with equal
amplitude, wavelength and frequency
• Standing waves on a string is created
when a fixed string on both ends is
plucked.
– Results in travelling waves moving in opposite
directions

3. Standing Waves on Strings
• The wavelength of a standing wave is
dependent on the length of the string, L
and m which is a positive, nonzero integer:
• A smaller m gives the largest wavelength
and a larger m gives a smaller
wavelength.
– This provides standing waves that are called
normal modes of vibration of the string

4. Standing Waves on Strings
• Frequencies corresponding to the normal
modes of vibration are:
• A lower frequency will result in a larger
wavelength and is known as the
fundamental frequency or the first
harmonic

5. Application
• Notes made from a
piano are caused by
varying lengths, and
mass densities of the
strings. On each
opposite end of the
keyboard, there will
be a different mass
density and length to
produce either a high
or a low frequency.

6. Application
Given the following information, determine the
wave speed, wavelength, frequency (for the
first harmonic) and conclude if the string
resonates for a lower note or a higher note.
• Length of string 1: 4.5m
• Mass density of string 1: 2.49*10-2kg/m
• Length of string 2: 1.5m
• Mass density of string 2: 4.12*10-4 kg/m
• The strings are held on a tension of 70.0NNote: Values are arbitrary and are not accurate
to what is actually found in a piano.

7. Solution
Wave speed for string 1:
Wavelength for string 1:
Frequency for string 1:

8. Solution (cont.)
Wave speed for string 2:
Wavelength for string 2:
Frequency for string 2:

9. Solution (cont.)
• Comparing the two frequencies:
– f1 = 5.88Hz
– f2 = 13.74Hz
• A lower frequency results in a lower pitched
sound and a higher frequency results in a
higher pitched sound.
• It can be concluded that string 1 pertains to a
lower note and string 2 pertains to a higher
note.
– This can be verified by looking at the wave speed
and wave lengths of each string.