1. Standing Waves

2. Two pulses are shown traveling in
opposite directions along a string.
Each is moving with a velocity of
1.0 cm/s. After 4.0 s, the string will look like which diagram?
Ans: #2

3. f1 = v/2L for a fixed string so f1 = 692.8 m/s / (2*0.80m) = 433 Hz
A guitar string 80.0 cm long has a mass of 25.0 g. When tuned it is under a tension force of 15 kN. What will be the fundamental frequency of this string when played? What will be the next 3 harmonic frequencies for this string?
Need to know the velocity. v = √ F/μ
Then find the fundamental frequency.
v = √15 x 103 N / (.025 kg/.80 m) = m/s
f1 = v/2L for a fixed string so f1 = m/s / (2*0.80m) = 433 Hz
A fixed string produces all harmonics so the next 3 will be:
f2 = 2(433 Hz) f3 = 3(433 Hz) f4 = 4(433 Hz)

4. A stretched string is fixed at points 1 and 5
A stretched string is fixed at points 1 and 5. When vibrating at the 2nd harmonic frequency, the nodes of the standing wave are at points:
1,3 and 5
If the string is 1.5 m long and a wave will travel at 300 m/s,
what is the frequency of the 2nd harmonic?
The fundamental, f1 = v/2L so f1 = 100 Hz. A fixed string
produces all harmonics so the 2nd, f2 = 2(f1) or 200 Hz.

5. The figure represents a string of length L, fixed at both ends,
vibrating in several harmonics.
The 4th harmonic is shown in: ___
This represents the ? overtone.
The 5th harmonic is: #4
3rd #5

6. closed #4 #2 Not here #3 The figure represents a column of
length L, Vibrating in several
harmonics. Is this a closed or
open end instrument?
The 7th harmonic is:
The first overtone is:
The 4th harmonic is:
The second overtone is:
closed #4 #2
Not here #3

7. Identify the harmonic and overtone in each diagram. none
Of the sound sources shown, which is vibrating with its first harmonic:
Its third harmonic:
The 2nd harmonic:
Identify the harmonic and overtone in each diagram.
none
The rod and whistle
Not here
Whistle: 3rd H, 1st O pipe: 2nd H, 1st O string: 2nd H, 1st O rod: 3rd H, 1st O

8. Standing waves exist in a closed-end pipe of length L
Standing waves exist in a closed-end pipe of length L. The speed of the waves on the string is v. The three lowest frequencies of vibration are:
a. v/4L v/2L 3v/4L
b. v/4L v/4L v/4L
c. v/2L v/2L v/2L
d. v/L 2v/2L 2v/3L

9. Which pipe shown will produce the lowest pitch?
closed open closed open
L = 1.0 m L = 1.0 m L = 0.5 m L = 0.5 m
Ans: must produce the longest λ so
the 1.0 m closed pipe
Remember: closed starts with ¼ λ