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Oscillations, waves and sound exercises · Physics Playground

ExercisesPhysics

Oscillations, waves and sound

51 problems with worked solutions, from Physics and College Physics.

Start with a random one

Learn it first: Springs & Oscillations, Waves

Physics13.2 Wave Properties: Speed, Amplitude, Frequency, and Period

ExampleCalculate the Velocity of Wave Propagation: Gull in the OceanCalculate the wave velocity of the ocean wave in the previous figure if the distance between wave crests is 10.0 m and the time for a seagull to bob up and down is 5.00 s.
ExampleCalculate the Period and the Wave Velocity of a Toy Spring (part 1)The woman in Figure 13.3 creates two waves every second by shaking the toy spring up and down. (a)What is the period of each wave? (b) If each wave travels 0.9 meters after one complete wave cycle, what is the…

Physics14.1 Speed of Sound, Frequency, and Wavelength

ExampleWhat Are the Wavelengths of Audible Sounds?Calculate the wavelengths of sounds at the extremes of the audible range, 20 and 20,000 Hz, in conditions where sound travels at 348.7 m/s.

Physics14.2 Sound Intensity and Sound Level

ExampleCalculating Sound Intensity Levels: Sound WavesCalculate the sound intensity level in decibels for a sound wave traveling in air at 0 ºC and having a pressure amplitude of 0.656 Pa.
ExampleChange Intensity Levels of a Sound: What Happens to the Decibel Level?Show that if one sound is twice as intense as another, it has a sound level about 3 dB higher.

Physics14.3 Doppler Effect and Sonic Booms

ExampleCalculate Doppler Shift: A Train HornSuppose a train that has a 150 Hz horn is moving at 35 m/s in still air on a day when the speed of sound is 340 m/s. What frequencies are observed by a stationary person at the side of the tracks as the train…

Physics14.4 Sound Interference and Resonance

ExampleFinding the Length of a Tube for a Closed-Pipe ResonatorIf sound travels through the air at a speed of 344 m/s, what should be the length of a tube closed at one end to have a fundamental frequency of 128 Hz?
ExampleFinding the Third Overtone in an Open-Pipe ResonatorIf a tube that’s open at both ends has a fundamental frequency of 120 Hz, what is the frequency of its third overtone?
ExampleUsing Beat Frequency to Tune a PianoPiano tuners use beats routinely in their work. When comparing a note with a tuning fork, they listen for beats and adjust the string until the beats go away (to zero frequency). If a piano tuner hears two beats per…

College Physics16.1 Hooke’s Law: Stress and Strain Revisited

Example 16.1How Stiff Are Car Springs?Figure 16.5 The mass of a car increases due to the introduction of a passenger. This affects the displacement of the car on its suspension system. (credit: exfordy on Flickr) What is the force constant for the…With a figure
Example 16.2Calculating Stored Energy: A Tranquilizer Gun SpringWe can use a toy gun’s spring mechanism to ask and answer two simple questions: (a) How much energy is stored in the spring of a tranquilizer gun that has a force constant of 50.0 N/m and is compressed 0.150 m? (b)…With a figure
Quick checkEnvision holding the end of a ruler with one hand and deforming it with the other. When you let go, you can see the oscillations of the ruler. In what way could you modify this simple experiment to increase the…
Quick checkIf you apply a deforming force on an object and let it come to equilibrium, what happened to the work you did on the system?

College Physics16.2 Period and Frequency in Oscillations

Example 16.3Determine the Frequency of Two Oscillations: Medical Ultrasound and the Period of Middle CWe can use the formulas presented in this module to determine both the frequency based on known oscillations and the oscillation based on a known frequency. Let’s try one example of each. (a) A medical imaging device…
Quick checkIdentify an event in your life (such as receiving a paycheck) that occurs regularly. Identify both the period and frequency of this event.

College Physics16.3 Simple Harmonic Motion: A Special Periodic Motion

Example 16.4Calculate the Frequency and Period of Oscillations: Bad Shock Absorbers in a CarIf the shock absorbers in a car go bad, then the car will oscillate at the least provocation, such as when going over bumps in the road and after stopping (See Figure 16.10). Calculate the frequency and period of…
Quick checkSuppose you pluck a banjo string. You hear a single note that starts out loud and slowly quiets over time. Describe what happens to the sound waves in terms of period, frequency and amplitude as the sound decreases…
Quick checkA babysitter is pushing a child on a swing. At the point where the swing reaches x, where would the corresponding point on a wave of this motion be located?

College Physics16.4 The Simple Pendulum

Quick checkAn engineer builds two simple pendula. Both are suspended from small wires secured to the ceiling of a room. Each pendulum hovers 2 cm above the floor. Pendulum 1 has a bob with a mass of 10kg. Pendulum 2 has a bob…

College Physics16.5 Energy and the Simple Harmonic Oscillator

Example 16.6Determine the Maximum Speed of an Oscillating System: A Bumpy RoadSuppose that a car is 900 kg and has a suspension system that has a force constant k=6.53×10^4N/m. The car hits a bump and bounces with an amplitude of 0.100 m. What is its maximum vertical velocity if you assume no…
Quick checkWhy does it hurt more if your hand is snapped with a ruler than with a loose spring, even if the displacement of each system is equal?
Quick checkYou are observing a simple harmonic oscillator. Identify one way you could decrease the maximum velocity of the system.

College Physics16.6 Uniform Circular Motion and Simple Harmonic Motion

Quick checkIdentify an object that undergoes uniform circular motion. Describe how you could trace the simple harmonic motion of this object as a wave.

College Physics16.7 Damped Harmonic Motion

Example 16.7Damping an Oscillatory Motion: Friction on an Object Connected to a SpringDamping oscillatory motion is important in many systems, and the ability to control the damping is even more so. This is generally attained using non-conservative forces such as the friction between surfaces, and…With a figure
Quick checkWhy are completely undamped harmonic oscillators so rare?
Quick checkDescribe the difference between overdamping, underdamping, and critical damping.

College Physics16.8 Forced Oscillations and Resonance

Quick checkA famous magic trick involves a performer singing a note toward a crystal glass until the glass shatters. Explain why the trick works in terms of resonance and natural frequency.

College Physics16.9 Waves

Example 16.8Calculate the Velocity of Wave Propagation: Gull in the OceanCalculate the wave velocity of the ocean wave in Figure 16.30 if the distance between wave crests is 10.0 m and the time for a sea gull to bob up and down is 5.00 s.
Quick checkWhy is it important to differentiate between longitudinal and transverse waves?

College Physics16.10 Superposition and Interference

Quick checkImagine you are holding one end of a jump rope, and your friend holds the other. If your friend holds her end still, you can move your end up and down, creating a transverse wave. If your friend then begins to move…
Quick checkDefine nodes and antinodes.
Quick checkYou hook up a stereo system. When you test the system, you notice that in one corner of the room, the sounds seem dull. In another area, the sounds seem excessively loud. Describe how the sound moving about the room…

College Physics16.11 Energy in Waves: Intensity

Example 16.9Calculating intensity and power: How much energy is in a ray of sunlight?The average intensity of sunlight on Earth’s surface is about 700W/m^2. (a) Calculate the amount of energy that falls on a solar collector having an area of 0.500m^2 in 4.00h. (b) What intensity would such sunlight…
Example 16.10Determine the combined intensity of two waves: Perfect constructive interferenceIf two identical waves are spatially separated, each having an intensity of 1.00 W/m2, interfere perfectly constructively in a particular location, what is the intensity of the wave at this particular location?
Quick checkWhich measurement of a wave is most important when determining the wave's intensity?

College Physics17.2 Speed of Sound, Frequency, and Wavelength

Example 17.1Calculating Wavelengths: What Are the Wavelengths of Audible Sounds?Calculate the wavelengths of sounds at the extremes of the audible range, 20 and 20,000 Hz, in 30.0ºC air. (Assume that the frequency values are accurate to two significant figures.)
Quick checkImagine you observe two fireworks explode. You hear the explosion of one as soon as you see it. However, you see the other firework for several milliseconds before you hear the explosion. Explain why this is so.
Quick checkYou observe two musical instruments that you cannot identify. One plays high-pitch sounds and the other plays low-pitch sounds. How could you determine which is which without hearing either of them play?

College Physics17.3 Sound Intensity and Sound Level

Quick checkDescribe how amplitude is related to the loudness of a sound.
Quick checkIdentify common sounds at the levels of 10 dB, 50 dB, and 100 dB.

College Physics17.4 Doppler Effect and Sonic Booms

Example 17.4Calculate Doppler Shift: A Train HornSuppose a train that has a 150-Hz horn is moving at 35.0 m/s in still air on a day when the speed of sound is 340 m/s. (a) What frequencies are observed by a stationary person at the side of the tracks as the train…
Quick checkWhy did scientist Christian Doppler observe musicians both on a moving train and also from a stationary point not on the train?
Quick checkDescribe a situation in your life when you might rely on the Doppler shift to help you either while driving a car or walking near traffic.

College Physics17.5 Sound Interference and Resonance: Standing Waves in Air Columns

Example 17.5Find the Length of a Tube with a 128 Hz Fundamental(a) What length should a tube closed at one end have on a day when the air temperature, is 22.0ºC, if its fundamental frequency is to be 128 Hz (C below middle C)? (b) What is the frequency of its fourth overtone?
Quick checkDescribe how noise-canceling headphones differ from standard headphones used to block outside sounds.
Quick checkHow is it possible to use a standing wave's node and antinode to determine the length of a closed-end tube?

College Physics17.6 Hearing

Example 17.6Measuring Loudness: Loudness Versus Intensity Level and Frequency(a) What is the loudness in phons of a 100-Hz sound that has an intensity level of 80 dB? (b) What is the intensity level in decibels of a 4000-Hz sound having a loudness of 70 phons? (c) At what intensity level will…
Quick checkAre ultrasound and infrasound imperceptible to all hearing organisms? Explain your answer.

College Physics17.7 Ultrasound

Example 17.7Calculate Acoustic Impedance and Intensity Reflection Coefficient: Ultrasound and Fat Tissue(a) Using the values for density and the speed of ultrasound given in Table 17.5, show that the acoustic impedance of fat tissue is indeed 1.34×10^6kg/(m^2·s). (b) Calculate the intensity reflection coefficient of…
Example 17.8Calculate Velocity of Blood: Doppler-Shifted UltrasoundUltrasound that has a frequency of 2.50 MHz is sent toward blood in an artery that is moving toward the source at 20.0 cm/s, as illustrated in Figure 17.47. Use the speed of sound in human tissue as 1540 m/s. (Assume…With a figure
Quick checkWhy is it possible to use ultrasound both to observe a fetus in the womb and also to destroy cancerous tumors in the body?