Answer all questions either in the spaces provided or on a separate sheet of paper. Remember to employ proper problem-solving techniques throughout. You must show all work, including equations, substitutions, and units.
Useful Equations and Concepts
vwave = fL
vwave = L/T
f = 1/T
vwave = sqrt[T/(m/l)]
All Waves
Transverse Wave in a String or Rope Under Tension
where vwave is the velocity of the wave (m/s), f is frequency (Hz),
L is wavelength (m), T is period (s), and t is air temperature (degrees C).
where vwave is the velocity of the wave (m/s), m is mass (kg), l is string length (m) and T is tension (N).
Velocities of Sound in Selected Substances (m/s)
Gases (at 0 degrees C)
Carbon Dioxide
Air
Helium
Liquids (at 25 degrees C)
Ethyl Alcohol
Water (pure)
Water (seawater)
Solids
Lead
Wood
Iron and Steel
Aluminum
Glass
259
331
965
1207
1498
1531
1200
4300
5000
5100
5170
Sound Waves
B = 10 log (I/Io)
f = fo(v/v - vs)
f = fo(v/v + vs)
Intensity
Doppler shift
(for source approaching observer)
(for source receding from observer)
where f is frequency of source (Hz), fo is observed
frequency (HZ), v is wave velocity in medium (m/s),
vsis relative velocity of the source (m/s).
where B is intensity in decibels (dB), I is intensity (watt/mexp2),
Io is 10exp-12 (watt/mexp2)
1. Calculate the length of a sound wave which possesses a frequency of 350 Hz and is traveling through air at a temperature of 15 degrees C.
2. A stretched string has a length of 1.5 m and a mass of 0.25 kg. Calculate the necessary string tension for the string to produce waves with a velocity of 5 m/s when plucked.
3. Calculate the length of a sound wave which possesses a frequency of 300 Hz and is traveling through an air temperature of 20 degrees C.
4. Calculate the period of a wave with a frequency of 12,000 Hz.
5. Calculate the distance from a sound source to an observer if the waves require 3 s of travel time through 25 degrees C air.
6. Calculate the intensity factor between a 100-dB source and a 60-dB source.
7. A train whistle possesses a natural frequency 1500 Hz. If the train is approaching a station at a velocity of 30 m/s, calculate the frequency of the whistle perceived by an observer standing at the station, given an air temperature of 30 degrees C.
