# 11.3.3.3: Problems

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Exercise $$\PageIndex{1}$$: A slow-motion representation of a sound wave propagating in Lucite

The animation is a slow-motion representation of a cross section of a sound wave propagating in Lucite. A detector, the orange square, is placed in the pipe and properly measures the pressure (position is given in meters and time is given in seconds). What is the speed of the sound wave? Note: The animation runs for $$0.1\text{ s}$$. Press "reset" to reload the animation. Restart.

Exercise $$\PageIndex{2}$$: The animation represents a sound wave propagating in a very long pipe

The animation represents a cross section of a sound wave propagating in a very long pipe. Restart. A detector, the orange square, is placed in the pipe and properly measures the pressure (position is given in meters and time is given in milliseconds). Which of the graphs properly represents the displacement of the air molecules in the pipe?

Exercise $$\PageIndex{3}$$: Why are there no dead spots?

Why are there no dead spots in the sound distribution (position is given in centimeters and time is given in seconds) when either the left or the right source is transmitting, but there are multiple dead spots when both sources are transmitting?

Exercise $$\PageIndex{4}$$: A standing wave on a string

The animation shows a standing wave on a string (position is given in centimeters and time is given in seconds). If this string is on a musical instrument, what wavelength sound is produced by the standing wave? Restart.

Exercise $$\PageIndex{5}$$: A standing wave on a stringed musical instrument

The animation shows a standing wave on a stringed musical instrument (position is given in centimeters and time is given in seconds). If the tension in this string is doubled and the string stays in its fundamental mode, what frequency sound is produced by the new standing wave? Restart.

Exercise $$\PageIndex{6}$$: What is the difference in frequency between the two waves?

The animation shows a superposition of two waves on identical strings (position is given in meters and time is given in seconds). What is the difference in frequency between the two waves? Restart.

Exercise $$\PageIndex{7}$$: A man and woman in front of the White House hear a siren as an ambulance drives by

A man and a woman are in front of the White House as an ambulance drives by with its sirens on (position is given in meters and time is given in seconds). Restart.

The three animations play the possible siren sound heard by three individuals: the man, the woman and the ambulance driver.

1. The sound in Animation 1 is heard by whom?
2. The sound in Animation 2 is heard by whom?
3. The sound in Animation 3 is heard by whom?

Problem authored by Morten Brydensholt, Wolfgang Christian, and Mario Belloni.
Script authored by Morten Brydensholt, Wolfgang Christian, and Mario Belloni.

Exercise $$\PageIndex{8}$$: In which of the animation(s) does the source travel slower than sound?

The animation represents a cross section of a three-dimensional sound wave propagating away from a moving source (time is given in seconds)Restart.

1. In which of the animation(s) does the source travel slower than the speed of sound?
2. In which of the animation(s) does the resulting sound wave travel the fastest?

Exercise $$\PageIndex{9}$$: Which of the following animations represents what you would hear?

You are standing beside a highway as a police car with its siren on drives by, as shown in the animation (position is given in meters and time is given in seconds)Restart. Which of the animations represents what you would hear?

Exercise $$\PageIndex{10}$$: Determine the change in frequency you will hear as the police car goes by

You are standing beside a highway as a police car with its siren on drives by, as shown in the animation (position is given in meters and time is given in seconds). If the frequency of the siren is $$800\text{ Hz}$$, determine the change in frequency you will hear as the police car goes by. Restart.

Exercise $$\PageIndex{11}$$: Using a speaker, a standing sound wave has been set up inside a tube

Using a speaker, a standing sound wave has been set up inside a tube. A movable microphone lies inside the tube (position is given in meters and time is given in seconds). The graph shows the sound recorded by the microphone as a function of time. Move the microphone back and forth to study the changing amplitude of the sound it receives. Restart.

1. For what microphone position(s) does the amplitude of the sound go to zero? What is such a location called?
2. For what microphone position(s) is the amplitude of the sound a maximum? What is such a location called?
3. From the locations of the nodes, determine the wavelength of the sound waves.
4. From the graph, determine the frequency of the sound waves.
5. Using the wavelength and the frequency, find the velocity of the sound waves in the tube.

Problem authored by Steve Mellema and Chuck Niederriter.
Script authored by Steve Mellema and Chuck Niederriter.

Exercise $$\PageIndex{12}$$: A standing wave in an open pipe

This animation shows a standing wave in an open pipe (position is given in centimeters and time is given in seconds). Restart.

1. In which harmonic, $$n$$, is the air in the pipe oscillating?
2. Determine the frequency of the musical tone produced by the pipe in this situation.
3. Determine the fundamental frequency of the pipe (lowest frequency of resonance).

Problem authored by Morten Brydensholt, Wolfgang Christian, and Mario Belloni.

Exercise $$\PageIndex{13}$$: A standing wave in an open pipe

The animation shows a standing wave in an open pipe (position is given in centimeters and time is given in seconds). Restart.

1. In which harmonic, $$n$$, is the air in the pipe oscillating?
2. Determine the frequency $$f_{n}$$ of the tone produced by the pipe in this situation.
3. Determine the frequency of the eighth harmonic $$f_{8}$$.
4. Determine the speed of sound $$v$$.

Problem authored by Morten Brydensholt, Wolfgang Christian, and Mario Belloni.

Exercise $$\PageIndex{14}$$: A standing wave in a half-open pipe

The animation shows a standing wave in a half-open pipe (position is given in centimeters and time is given in seconds). Restart.

1. In which harmonic, $$n$$, does the air in the pipe oscillate?
2. Determine the frequency $$f_{n}$$ of the tone produced by the pipe in this situation.
3. Determine the fundamental frequency $$f_{1}$$ (the lowest frequency of resonance in the pipe).
4. Determine the speed of sound $$v$$.

Problem authored by Morten Brydensholt, Wolfgang Christian, and Mario Belloni.

Exercise $$\PageIndex{15}$$: A standing wave in a half-open pipe

This animation shows a standing wave in a half-open pipe (position is given in centimeters and time is given in seconds). Restart.

1. Determine the frequency $$f_{n}$$ of the tone produced by the pipe in this situation.
2. Now the pipe is cut into two pieces of equal length. Determine the fundamental frequency of each of the two pieces.

Problem authored by Morten Brydensholt, Wolfgang Christian, and Mario Belloni.

Exercise $$\PageIndex{16}$$: A standing wave in a half-open pipe

This animation shows a standing wave in a half-open pipe (position is given in centimeters and time is given in seconds). Restart.

1. In which harmonic, $$n$$, is the air in the pipe oscillating?
2. Determine the wavelength for this oscillation.

Problem authored by Morten Brydensholt, Wolfgang Christian, and Mario Belloni.

Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.

This page titled 11.3.3.3: Problems is shared under a CC BY-NC-ND license and was authored, remixed, and/or curated by Wolfgang Christian, Mario Belloni, Anne Cox, Melissa H. Dancy, and Aaron Titus, & Thomas M. Colbert.