SME
Grade 11 Science · Problem type
A standing wave on a string
Use this for “A 0.65 m guitar string carries waves at 286 m/s. What frequency is its first harmonic?”
Diagram
λ = 2L/n = 2 × 0.65/1 = 1.3 m
f = v/λ = 286/1.3 = 220 Hz
2 nodes (N, no motion) and 1 antinode (A, the most motion).
The fixed ends are nodes.
This is an example. Type your own values to start a new problem.
λ (m)
=
2
×
L (m)
n
v (m/s)
=
f (Hz)
×
λ (m)
Formulas
λ
=
2
×
L
n
1.3 = 2 × 0.65/1
v
=
f
×
λ
286 = 220 × 1.3
Assumptions
•
Both ends are fixed, so they are nodes: harmonic n fits n half wavelengths, λ = 2L/n.
•
Nodes (N) never move; antinodes (A) swing the most.
•
The string’s tension and mass set the wave speed v.
Step-by-step
WE KNOW
n = 1, L = 0.65 m, v = 286 m/s
FIND
wavelength (λ), frequency (f)
Step 1 · Find wavelength (λ)
Use λ = 2 × L/n
Harmonic
n
fits
n
half
wavelengths
in
the
length.
λ
=
2
×
L
λ
=
2
×
0.65
λ
=
1.3
m
Step 2 · Find frequency (f)
Use v = f × λ
Waves
pass
at
v
;
each
is
λ
long:
v
λ
of
them
each
second.
f
=
v
λ
f
=
286/1.3
f
=
220
Hz
Check
Put the numbers back in. Both sides should match.
1.3 = 2 × 0.65/1 ✓
286 = 220 × 1.3 ✓
← Previous lesson
Waves and sound: wave properties, standing waves and the Doppler effect
Next lesson →
A pipe open at both ends
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
Related lessons
Waves and sound: wave properties, standing waves and the Doppler effect
Main lesson
A pipe open at both ends
Use this for “A 0.50 m flute-like pipe is open at both ends. What is its lowest note in 343 m/s air?”
A pipe closed at one end
Use this for “A 0.25 m tube is closed at the bottom. What is its lowest note in 343 m/s air, and the next one it can play?”
The Doppler effect
Use this for “A 700 Hz siren passes you at 25 m/s. What pitch do you hear as it comes and as it goes?”
Sound level in decibels
Use this for “A busy street has a sound intensity of 10⁻⁵ W/m². What is its sound level in decibels?”
Transverse or longitudinal?
Use this for “Is a sound wave transverse or longitudinal?”