Doppler Effect
1) A fire truck has a blaring siren with a frequency of 400 Hz. It approaches a stationary
listener with a speed of 25.0 m/s Calculate the Doppler frequency of the sound at 20.0 oC.
[431 Hz]
2) A sound source traveling at 2.50 x 10 2 m/s in 20.0 oC air emits a sound of frequency 128 Hz
as it approaches a point X. Estimate the frequency of the approaching sound as heard by a
stationary observer at X.[468 Hz]
3) A car traveling at 3.00 m/s in 0 oC air away from a stationary listener emits a horn
b1ast of frequency 100 Hz. What frequency does the listener detect? [99.1 Hz]
4) Two sound sources in 20 oC air moving towards each other at 1.2 x 102 m/s emit
identical frequencies of 1.8 x 102 Hz. A stationary observer midway between the sources
listens to the sounds. What frequency difference does she detect? [0 Hz]
5) A 350 Hz sound wave is emitted from a stationary source at 20.0 oC. An observer approaches
the source at 50.0 m/s. What will be the detected frequency? [401 Hz]
6) A 5.3 x 103 Hz sound wave leaves a stationary source and approaches a listener moving
towards the source at 17 m/s at 20.0 oC What is the observed frequency of the sound?
[5.6 x 103 Hz]
7) A stationary sound source at 20.0 oC emits a 500 Hz signal that is picked up by an observer
moving at 37.0 m/s away from the source. What is the detected frequency? [446 Hz]
8) A sound source in air at 0 oC emits a signal whose frequency is 390 Hz. What is the
frequency as detected by an observer moving away from the source at 25.0 m/s? [361 Hz]
Sound Speed
1) What is the speed of sound in air at 30 oC? [3.5 x 102 m/s]
2) What is the frequency of a sound wave of length 3.33 x 10-3 m in air at 15.0 oC?
[1.02 x 105 Hz]
3) The maximum frequency of human response to sound is 2.00 x 10 4 Hz. What is the
wavelength of the sound at 0 oC and at 20.0 oC? [1.66 x 10-2 m, 1.72 x 10-2 m]
4) Find the wavelength of sound of period 6.7 x 10-5 s in air at 35 oC. [2.4 cm]
5) A girl stands 0.65 km from the vertical wall of a cylindrical canyon and shouts at the wall. If
the air temperature is 30 oC, how long does it take her to hear her echo after she calls out?
[3.7 s]
6) A bat flying in 15.0 oC evening air uses sonar to locate a stationary juicy bug. If
the emitted sonar signal takes 8.50 x 10-2 s to return to the bat which is flying at 2.00 m/s
towards the bug, how long will it take the bat to catch the bug? [7.25 s]
7) A boy wanted to determine the distance of a vertical cliff face was from him. He shouted at
the cliff face and noted that his echo returned after 1.50 s. How far was the cliff from him, if
the air temperature was 25.0 oC? [260 m]
Waves in Strings
1) If a string vibrates with a fundamental frequency of 200 Hz, what are the frequencies of the
first three overtones? [400 Hz, 600 Hz, 800 Hz]
2) The wave speed in a stretched string is 4.5 x 10 2 m/s and the fundamental frequency of the
standing waves in the string is 3.0 x 102 Hz. Calculate the distance between the nodes.
[0.75 m]
3) Two successive overtones in a vibrating string are 175 Hz and 200 Hz. What is the frequency
of the second overtone? [75 Hz]
4) A 68 m rope is stretched between two trees on opposite sides of a river. The wave speed in
the rope is 3.4 x 102 m/s and the frequency is noted to be 50 Hz. Calculate the distance
between nodal points on the rope. How many nodes would the rope contain under these
circumstances? [3.4 m, 20 nodes]
5) A piano string is 1.20 m long and has a mass of 85 g. Calculate the tension in the string
when its fundamental frequency is 128 Hz.[6.7 x 103 N]
6) A 0.65 m guitar string of mass 32 g is stretched between two points and produces a
fundamental frequency of 250 Hz. Estimate the tension in the string.[5.2 x 10 3 N]
7) A 1.6 m plastic thread of mass 25 g is strung between two nails so that its fundamental
frequency is 87 Hz. Calculate the tension in the thread.[1.2 x 103 N]
8) Each end of a 1.5 m cord of mass 16 g is pulled hard by two boys. They note the tension in
the cord is 8.3 x 102 N. A girl plucks the cord. What is the frequency of the first harmonic?
[93 Hz]
9) A stretched piano string has a length of 2.3 m and a mass of 112 g. The string's measured
tension is 1.75 x 103 N. Calculate the frequency of the second harmonic. [82 Hz]
10) A cello string of mass 21 g and effective length 75 cm vibrates at 120 Hz. Predict its
frequency when the string is held firm by a finger at 25 cm from one end. [360 Hz]
Sound in Air Columns (Note: Use a speed of 330 m/s if not stated)
1) A 1.50 m pipe is open at both ends. What is the pipe's fundamental frequency? [110 Hz]
2) An 80.0 cm long tube is open at both ends. Calculate the frequency of the pipe's second
harmonic.[413 Hz]
3) A pipe is 1.20 m long and open at both ends. Calculate the frequency of the second overtone.
[413 Hz]
4) A tube is 14.0 m long and closed at one end. What is its fundamental frequency? [5.89 Hz]
5) A 2.5 m long pipe is open at one end only. Estimate its second harmonic. [99 Hz]
6) A cylindrical whistle is 10 cm long. Calculate the whistle's fundamental frequency.
[1.7 x 103 Hz]
7) Calculate the longest wavelength of the sound produced in a 75 cm long resonating tube
that is: a) open at one end only; b) open at both ends. [3.0 x 10 2 cm, 1.5 x 102 cm]
8) A 50.0 cm long tube closed at one end resonates at 167 Hz. What is the speed of sound?
[334 m/s]
9) A 1.50 m long tube is closed at one end. It vibrates with a fundamental frequency of 57.3 Hz
at 20.0 oC. On the basis of these data, estimate the speed of sound at 0 oC. [332 m/s]
10) A vibrating tuning fork is held at the open end of an air column of variable length. One end
of the air column is closed. As the air column's length is gradually increased, resonance first
occurs when the column is 16.1 cm long. What is the vibrating frequency of the tuning fork?
[516 Hz]
11) An air column that is open at both ends has a second overtone of wavelength 50 cm. What
is its fundamental frequency? [220 Hz]
12) A tube closed at one end has a third overtone at an air column length of 1.68 m. Find the
sound source’s frequency.[344 Hz]