Waves and Sound — Free Physics Review Games.

A wave is a disturbance that transfers energy from one point to another without transferring matter.

In transverse waves, particles vibrate perpendicular to the wave direction; in longitudinal waves, they vibrate parallel.

Frequency is measured in Hertz (Hz), representing the number of wave cycles per second.

Wavelength is the distance between two consecutive corresponding points on a wave, such as crest to crest.

Sound is a longitudinal wave that travels through a medium by compressing and rarefying particles.

The wave equation relates speed (v), frequency (f), and wavelength: v = f x wavelength.

The Doppler effect causes the observed frequency to increase as a source approaches and decrease as it recedes.

Sound requires a medium (solid, liquid, or gas) to propagate; it cannot travel through a vacuum.

Resonance occurs when an external force drives a system at its natural frequency, causing a dramatic increase in amplitude.

Amplitude is the maximum displacement from equilibrium and relates to the energy and intensity of a wave.

Constructive interference occurs when wave crests align, combining their amplitudes to create a larger wave.

Pitch is determined by frequency: higher frequency produces a higher pitch, lower frequency produces a lower pitch.

wavelength = v/f = 340/440 = 0.77 m.

Standing waves form when two identical waves travel in opposite directions and interfere, creating nodes (no displacement) and antinodes (maximum displacement).

In solids, particles are packed closely together with strong intermolecular forces, allowing vibrations to transfer more rapidly.

The period is defined as the time it takes for one complete oscillation or wave cycle to occur at a fixed point, measured in seconds. The distance between two adjacent crests is the wavelength, not the period, so that choice describes a spatial rather than temporal quantity. Students should remember that period and frequency are reciprocals, \(T = \frac{1}{f}\), which links timing to repetition rate.

A crest is the point of maximum positive displacement above the resting position of the medium in a transverse wave. The lowest point below equilibrium is called a trough, not a crest, so that option describes the opposite feature. Recognizing crests and troughs helps students identify amplitude and wavelength directly from a wave diagram.

A node is a location on a standing wave where destructive interference causes the medium to have zero displacement at all times. Maximum displacement instead describes an antinode, which is the opposite behavior from a node. Knowing the alternating node-antinode pattern is essential for analyzing resonance in strings and air columns.

Sound waves are longitudinal because air molecules vibrate back and forth parallel to the direction the wave travels, creating compressions and rarefactions. A wave on a guitar string is transverse since the string moves perpendicular to the wave's direction of travel, making that choice incorrect. Students should associate longitudinal waves with compression-based motion, common in sound and seismic P-waves.

An echo occurs because sound waves reflect off a hard, rigid surface and travel back toward their origin, obeying the law of reflection for waves. Complete absorption would eliminate any returning sound, which contradicts the very definition of an echo. This reflection behavior is a general wave property that also applies to light and water waves hitting boundaries.

Ultrasound refers to sound waves with frequencies greater than about \(20{,}000\ \text{Hz}\), exceeding the upper limit of typical human hearing. Sound below the audible range is called infrasound, which is the opposite frequency extreme and therefore an incorrect description here. This distinction is useful for understanding medical imaging and animal communication that rely on frequencies outside human perception.

Mechanical waves like sound require particles of a medium to collide and transfer energy from one location to another, so a physical substance is necessary. A vacuum contains no particles to vibrate, which is why sound cannot propagate through empty space, making that choice incorrect. This contrasts with electromagnetic waves such as light, which can travel through a vacuum without any medium.

Infrasound consists of sound waves with frequencies lower than about \(20\ \text{Hz}\), below the threshold that human ears can detect. Frequencies above human hearing are called ultrasound, which is the opposite end of the spectrum and not what this term describes. Both infrasound and ultrasound illustrate that the audible range is only a small portion of the full sound frequency spectrum.

When crests align with crests, the displacements add together, producing a wave of greater amplitude, which defines constructive interference. Destructive interference instead occurs when a crest meets a trough and the displacements cancel, which is the opposite scenario described here. Understanding how waves combine according to superposition is fundamental to explaining beats, standing waves, and diffraction patterns.

Refraction is the bending of a wave as it changes speed while crossing the boundary between two different media, such as light entering water or sound entering warmer air. Reflection instead describes a wave bouncing back off a surface rather than continuing into a new medium, so it does not match the bending behavior described. Refraction depends on the change in wave speed between media, a concept that applies broadly to sound, light, and water waves.

Using the wave equation \(v = f\lambda\), multiplying \(5\ \text{Hz}\) by \(2\ \text{m}\) gives a speed of \(10\ \text{m/s}\). The value \(2.5\ \text{m/s}\) incorrectly results from dividing frequency by wavelength instead of multiplying them together. Students should always confirm they are multiplying, not dividing, when applying the wave equation to find speed.

As the source approaches, successive wave fronts are compressed into a shorter distance, increasing the observed frequency according to the Doppler effect. A lower perceived frequency would instead occur if the source were moving away from the observer, which is the opposite motion described in this scenario. This shift explains why sirens sound higher-pitched approaching and lower-pitched receding, a hallmark application of the Doppler effect.

The beat frequency equals the absolute difference between the two source frequencies, so \(260\ \text{Hz} - 256\ \text{Hz} = 4\ \text{Hz}\). The value \(516\ \text{Hz}\) incorrectly results from adding the frequencies together rather than subtracting them, which does not represent how beats form. Beats arise from periodic constructive and destructive interference between two close frequencies, a key concept in tuning musical instruments.

When the singer's note matches the natural resonant frequency of the glass, energy is transferred efficiently, causing the amplitude of vibration to grow large enough to break the glass. Loudness alone does not explain the shattering, because even a quiet tone at the resonant frequency can build up significant amplitude over time through repeated energy transfer. This demonstrates resonance, where matching frequencies produce dramatically amplified oscillations compared to non-matching frequencies.

Superposition states that when multiple waves overlap in the same medium, the net displacement at any point equals the algebraic sum of the displacements each wave would produce individually. The claim that waves always cancel is incorrect because interference can be constructive, destructive, or somewhere in between depending on phase relationships. This principle underlies interference patterns, beats, and standing waves across all types of wave phenomena.

As temperature rises, air molecules gain kinetic energy and move faster, allowing sound wave disturbances to be transmitted between molecules more quickly, increasing wave speed. The idea that warmer air is less dense and therefore slows sound is misleading because the dominant effect of temperature is on molecular speed, not density-driven slowing. This relationship explains why sound travels roughly \(343\ \text{m/s}\) at room temperature but somewhat slower in colder air.

For a string fixed at both ends vibrating in its fundamental mode, the string length equals half a wavelength, so the wavelength is \(2L = 2(0.65\ \text{m}) = 1.3\ \text{m}\). The choice \(0.65\ \text{m}\) mistakenly equates the wavelength directly to the string length instead of doubling it as the fundamental mode requires. Recognizing that the fundamental mode of a string fits exactly half a wavelength is essential for solving standing wave problems.

Amplitude corresponds to the intensity of energy carried by the wave, and greater amplitude is perceived by listeners as increased loudness. Pitch is instead determined by frequency, not amplitude, so that option confuses two distinct properties of sound. Students should keep amplitude linked to loudness and frequency linked to pitch to avoid mixing up these separate wave characteristics.

Because water molecules are much closer together than air molecules, vibrations are passed from particle to particle more quickly, resulting in a higher speed of sound in water. The claim that water has lower density than air is factually incorrect, since water is far denser, and this misconception would actually predict the wrong trend. This principle generalizes to the rule that sound typically travels fastest in solids, slower in liquids, and slowest in gases due to differences in particle spacing and stiffness.

As the source moves away, successive wave crests are stretched farther apart, increasing the wavelength observed while decreasing the frequency detected, consistent with the Doppler effect. An increase in both frequency and wavelength is physically impossible for a fixed wave speed, since \(v = f\lambda\) requires them to change inversely, ruling out that option. This inverse relationship between frequency and wavelength under Doppler shifting is key to solving related motion problems.

Wave intensity depends on the energy transported by the wave, and since energy scales with the square of amplitude, intensity is proportional to amplitude squared, \(I \propto A^2\). A simple direct proportionality would underestimate how strongly loudness or brightness increases as amplitude grows, making that choice inaccurate. This squared relationship explains why even modest increases in amplitude can produce large increases in perceived loudness or brightness.

The decibel scale quantifies sound intensity level using a logarithmic scale because human perception of loudness spans an enormous range of intensities. Frequency is instead measured in hertz, a completely separate unit describing pitch rather than loudness, so that option misidentifies what decibels represent. Using a logarithmic scale allows manageable numbers to represent the vast range from a whisper to a jet engine.

When the length of the air column matches a condition that supports a standing wave at the tuning fork's frequency, resonance occurs and the sound intensity increases dramatically. Destructive interference cannot amplify a wave, since by definition it reduces amplitude through cancellation, making that choice inconsistent with the described loudness increase. This resonance tube setup is a classic method for determining the speed of sound experimentally.

Pitch is a perceptual quality directly tied to the frequency of the sound wave, with higher frequencies producing higher perceived pitch. Amplitude instead affects loudness rather than pitch, so changing amplitude alone would not change how high or low a tone sounds. This distinction between frequency-based pitch and amplitude-based loudness is fundamental to understanding how humans perceive sound.

Low-frequency sound waves have long wavelengths and can carry substantial energy over distance, creating pressure fluctuations strong enough to be physically felt as well as heard. Sound of any frequency in air travels at essentially the same speed, so claiming that bass sound travels faster is incorrect and not why it can be felt. This is a practical illustration that low frequencies correspond to long wavelengths, a relationship dictated by \(v = f\lambda\) at constant wave speed.

When the observer moves toward a stationary source, they encounter wave fronts more frequently, so the observed frequency increases according to \(f = f_0\left(\frac{v+v_o}{v}\right)\). The formula \(f = f_0\left(\frac{v - v_o}{v}\right)\) would incorrectly predict a decrease in frequency, which contradicts the fact that moving toward a source raises the perceived frequency. Correctly applying the Doppler formula requires matching the sign convention to the direction of relative motion between source and observer.

The \(n\)th harmonic on a string fixed at both ends has \(n+1\) nodes total, so the third harmonic has \(3+1=4\) nodes including the two fixed endpoints. Choosing \(3\) nodes would actually correspond to the second harmonic pattern, not the third, illustrating the importance of correctly counting nodes per harmonic number. Understanding this node-counting pattern is essential for identifying harmonic order from diagrams of standing waves on strings.

For a pipe closed at one end, the fundamental wavelength is four times the pipe length, so \(\lambda = 4(0.85\ \text{m}) = 3.4\ \text{m}\), giving \(f = \frac{v}{\lambda} = \frac{340}{3.4} = 100\ \text{Hz}\). The value \(200\ \text{Hz}\) mistakenly applies the open-open pipe relationship, where the wavelength is twice the length rather than four times the length. Distinguishing between open-open and closed-open pipe boundary conditions is critical, since closed pipes only support odd harmonics.

A path difference equal to a whole number of wavelengths means the two waves arrive in phase, so their crests align and they add constructively, producing a louder sound. Destructive interference instead requires a path difference of a half-integer number of wavelengths, which is not the case described here, making that option incorrect. This principle of path difference determining interference type is essential for analyzing speaker arrangements and double-slit-like acoustic setups.

Since \(v = \sqrt{T/\mu}\), quadrupling the tension \(T\) gives $v_{new} = \sqrt{4T/\mu} = 2\sqrt{T/\mu}$, meaning the speed doubles rather than scaling linearly with tension. Claiming the speed quadruples ignores the square root relationship between speed and tension, treating the formula as if it were linear instead. This square root dependence is important when analyzing how tuning a stringed instrument by adjusting tension affects the pitch produced.

Both the observer moving toward the source and the source moving toward the observer independently raise the perceived frequency, so the numerator uses \(v+v_o\) and the denominator uses \(v-v_s\), giving \(f = f_0\left(\frac{v+v_o}{v-v_s}\right)\). The expression \(f = f_0\left(\frac{v-v_o}{v+v_s}\right)\) incorrectly reverses both signs, which would model both parties moving apart rather than toward each other. Correctly assigning signs based on whether motion increases or decreases the relative approach speed is the key skill in general Doppler problems.

For an open-open pipe, all integer harmonics are present, so the second overtone corresponds to the third harmonic, giving \(3 \times 256\ \text{Hz} = 768\ \text{Hz}\). The value \(512\ \text{Hz}\) is actually the first overtone, or second harmonic, and mistakenly skips ahead in overtone counting rather than reaching the second overtone. Students must remember that the first overtone is the second harmonic, so overtone numbering is always one step behind harmonic numbering in open pipes.

The beat frequency, which corresponds to the rate of loudness maxima, equals the absolute difference between the two frequencies, \(442\ \text{Hz} - 438\ \text{Hz} = 4\ \text{Hz}\). The value \(440\ \text{Hz}\) incorrectly represents the average of the two frequencies rather than their difference, confusing perceived pitch with beat rate. Beats result from periodic constructive and destructive interference caused by the slight frequency mismatch between two nearly identical tones.

Marching in unison could apply a rhythmic force matching the bridge's natural resonant frequency, and repeated energy input at resonance can build oscillation amplitude to potentially damaging levels. The idea of avoiding a Doppler shift is irrelevant here, since the Doppler effect concerns frequency changes due to relative motion between source and observer, not structural vibration buildup. This scenario is a real-world illustration of mechanical resonance, where matching a driving frequency to a natural frequency can lead to catastrophic amplitude growth.

For a receding source, \(f = f_0\left(\frac{v}{v+v_s}\right) = 600\left(\frac{340}{374}\right) \approx 545\ \text{Hz}\), showing the perceived frequency drops below the emitted value. The choice \(660\ \text{Hz}\) would result from applying the approaching-source formula instead, which incorrectly raises rather than lowers the frequency for a source moving away. Choosing the correct sign in the Doppler denominator based on whether the source approaches or recedes is essential to avoid this common error.

A pipe closed at one end must have a node at the closed end and an antinode at the open end, a boundary condition that mathematically permits only odd harmonics such as the first, third, and fifth. An open-open pipe instead supports all integer harmonics because both ends require antinodes, making that option fundamentally different in its harmonic content. Recognizing which boundary conditions restrict harmonics to odd numbers only is crucial for correctly predicting resonant frequencies of wind instruments like clarinets.

Since power is proportional to \(A^2 f^2\), doubling both amplitude and frequency gives a factor of \(2^2 \times 2^2 = 4 \times 4 = 16\) increase in energy transport rate. A factor of \(4\) would result from doubling only one of the two variables, such as amplitude alone, rather than both simultaneously as stated in the problem. This combined dependence on amplitude squared and frequency squared shows how sensitive wave energy is to changes in these two fundamental properties.

Wavelength is defined as the spatial distance between two successive points in a wave that are in the same phase, such as one crest to the next. The description of time for one oscillation instead defines the period, a temporal quantity distinct from the spatial measure of wavelength. Distinguishing wavelength as a distance and period as a time is fundamental before applying the wave equation \(v = f\lambda\).

In a transverse wave, the particles of the medium oscillate perpendicular to the direction the wave energy travels, as seen in waves on a string or electromagnetic waves. Sound waves are instead longitudinal, with particle motion parallel to wave travel, making that choice an incorrect match for the perpendicular motion described. Distinguishing transverse from longitudinal motion is a foundational skill for classifying any new wave phenomenon encountered on the exam.

Since wave energy is proportional to the square of amplitude, any loss of energy due to factors like friction or spreading out causes the amplitude to decrease correspondingly. An increasing amplitude would imply the wave is gaining energy, which contradicts the premise that the wave is losing energy as it travels. This energy-amplitude relationship explains why sounds and other waves grow quieter or weaker the farther they travel from their source.

Frequency measures how many complete wave cycles occur at a fixed point per unit time, typically expressed in hertz where \(1\ \text{Hz} = 1\) cycle per second. Period instead measures the time for a single cycle rather than the count of cycles per second, making it the inverse relationship rather than the same quantity. Remembering that frequency counts events per time while period measures time per event helps avoid confusing these two related terms.

Each instrument produces a unique blend of overtones layered on top of the same fundamental frequency, and this distinct combination of harmonics creates the characteristic timbre that lets listeners distinguish instruments. The claim about differing sound speeds through air is incorrect because sound speed in a given medium depends on the medium's properties, not on which instrument produced the sound. This concept of timbre resulting from overtone content explains why two instruments can play identical pitches yet sound completely different.

Since \(f = \frac{1}{T} = \frac{1}{2\ \text{s}} = 0.5\ \text{Hz}\), applying \(v = f\lambda\) gives \(v = 0.5 \times 3\ \text{m} = 1.5\ \text{m/s}\). The value \(6\ \text{m/s}\) mistakenly multiplies the period directly by the wavelength instead of first converting period to frequency. Converting period to frequency before applying the wave equation is a common step students must remember when speed problems provide period rather than frequency.

Resonance occurs when a periodic driving force matches the natural frequency of a system, and pushing a swing in time with its natural oscillation period causes energy to accumulate, increasing the swing's amplitude. Turning up a radio's volume simply increases sound amplitude directly through the speaker rather than relying on any frequency-matching effect, so it does not illustrate resonance. Recognizing resonance in familiar systems like swings, bridges, and musical instruments helps connect abstract wave concepts to real experiences.

For an approaching source, \(f = f_0\left(\frac{v}{v - v_s}\right) = 300\left(\frac{340}{320}\right) \approx 319\ \text{Hz}\), confirming the perceived pitch rises as the source nears the observer. The value \(283\ \text{Hz}\) incorrectly applies the receding-source formula, adding rather than subtracting the source speed from the sound speed in the denominator. Correctly selecting the denominator sign based on the direction of source motion is essential to avoid inverting the expected pitch shift.