Pipes (no end correction)
A pipe open at both ends has length 0.50 m.
Calculate the fundamental frequency.
(v=343 m/s)
λ=2L=1.00m
f=343 Hz
A pipe has diameter 3.0 cm.
Calculate the end correction.
e=0.3d=0.009m
A bottle has a cylindrical neck with diameter 2.0 cm.
Calculate the cross‑sectional area of the neck.
r=0.010m
A=πr2=3.14×10−4 m2
By what factor is the intensity of a 60 dB sound greater than the intensity of the quietest sound a human can hear?
10^6
In human voice production, what part of the system acts as the generator?
Larynx
A pipe open at one end and closed at the other has length 0.60 m.
Calculate the fundamental frequency.
Answer:
λ=4L=2.40 m
f=343/2.40≈143 Hz
A pipe open at both ends has physical length 1.20 m and diameter 4.0 cm.
Calculate the effective length.
e=0.012m
Leff=1.20+2e=1.224 m
A Helmholtz resonator has:
Calculate the resonance frequency.
f≈173Hz
By what factor is the intensity of a loud rock concert (105 dB) greater than the intensity of a quiet office (35 dB)?
10^7
Two people sing the same note at the same loudness, but one sounds like they are singing “ah” while the other sounds like “ee.”
What physical difference causes this?
Different vocal tract shapes, which change the formant frequencies.
A 0.75 m pipe is open at both ends. Calculate the third resonant frequency.
The third resonant frequency refers to the third frequency that would be amplified if you gradually increased the driving frequency on such a tube as we did in class.
Third resonant frequency for open-open is 3rd harmonic.
λ3=2(0.75)/3=0.5 m
f3 = 343/0.5 = 686 Hz
A pipe open at both ends has a physical length of 1.00 m and a diameter of 5.0 cm.
What is the effective length?
e = 0.3d = 0.015 m
L_eff = L + 2e = 1.00 + 0.030 = 1.03 m
A bottle has:
Assume the neck and cavity are cylindrical. Calculate the resonance frequency
A=πr^2=π(0.010)^2=3.14×10−4 m^2
V=πr^2h=π(0.050)^2(0.12)=9.42×10−4m^3
Leff=L+2e=0.060+0.012=0.072 m
f≈118Hz
A sound’s intensity increases by a factor of 250.
By how many decibels does the sound intensity level rise?
10log10(250)≈24 dB
Generally describe what a frequency spectrum of a voice looks like. How does the graph change when changing vowels but keeping the same pitch?
3 peaks where harmonics are emphasized. Same peaks are present when changing vowels, but different harmonics are emphasized due to the vocal tract resonances
A pipe open at one end and closed at the other has length 0.90 m. Calculate the third resonant frequency.
The third resonant frequency refers to the third frequency that would be amplified if you gradually increased the driving frequency on such a tube as we did in class.
Third resonant frequency for open-closed is 5th harmonic.
λ=5/4L=0.72m
f=343/0.72≈476 Hz
A pipe is open at one end and closed at the other. Its physical length is 0.85 m and its diameter is 4.0 cm.
What is the fundamental frequency?
End correction:
e=0.3d=0.3(0.040)=0.012 m
Effective length (one open end):
Leff=L+e=0.85+0.012=0.862 m
Fundamental wavelength (open–closed):
λ=4Leff=4(0.862)=3.45 m
Frequency:
f=343/3.45≈99 Hzf
A cylindrical bottle has the following dimensions:
The bottle initially contains no water. How much water volume must be added to the bottle so that the Helmholtz resonance frequency becomes 150 Hz?
V≈5.8×10−4 m^3
V_initial=pi(0.050)^2(0.12)=9.42×10−4 m^3
Vwater=Vinitial−Vtarget
Vwater=3.6×10−4 m^3
The sound in a library has an intensity of
I_library = 2.0×10−8 W/m^2 and an intensity level of 43 dB.
Busy street traffic has an intensity of
I2 = 3.0×10−5 W/m^2
What is the intensity level (in dB) of the busy street traffic?
75 dB
Two sounds have the same intensity level in dB, but one is at 50 Hz and the other is at 3000 Hz.
Which will typically be perceived as louder, and why?
The 3000 Hz sound, because human hearing is most sensitive at mid‑to‑high frequencies due to our ear canal resonance.