Standing wave on string

1. LO: Standing Waves
on Strings
March 8

2. ● Where wave is travelling between 2 fixed
points at maximum amplitude
● There are fixed points along the string
called nodes
● waves travel back and forth, reflected at
the ends
What is a standing wave?

3. ● Many instruments used standing wave
model to produce sounds, such as guitars
and violins.
● The wave on a string can move at
different frequencies to produce
different harmonics
Application

4. 1. A string on a guitar is 500cm long and
when it is plucked, the string vibrates at
200m/s. Find the wavelength and
frequency of the wave at 1st, 2nd, and
3rd harmonics.
2. What is the relation between the
different harmonics and frequency?
Question:

5. ● f=v/λ
● λ=2L/n
● v=200m/s
● L=0.5m
● n=harmonic number, such
that 1st harmonic has n=1;
2nd has n=2 and so on.
Relevant Equations and Breakdown

6. 1st harmonic:
λ =2L/n
=2(0.5m)
=1m
f1 =v/λ
=(200m/s)/1
m
=200Hz
Solution
2nd harmonic:
λ =2L/n
=2(0.5m)/2
=0.5m
f1 =v/λ
=(200m/s)/0.5
m
=400Hz

7. 3rd harmonic:
λ =2L/n
=2(0.5m)/3
=0.33m
f1 =v/λ
=(200m/s)/0.33
m
=600Hz
Solution
From the calculations
it is clear that there is
a linear relation
between the frequency
and harmonics. As
harmonic number
increase by 1, the
frequency doubles