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)]
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)
Liquids (at 25 degrees C)
Iron and Steel
B = 10 log (I/Io)
f = fo(v/v - vs)
f = fo(v/v + vs)
(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.