Properties of Wave Pulses and Waves - AP Physics 2

Two strings of different materials are connected. A continuous wave of frequency $f$ travels from string 1 into string 2, where the wave speed is smaller. Which statement best describes the frequency in string 2?
Answer: It is unchanged because the source sets the oscillation rate at the boundary. This question tests understanding of properties of wave pulses and waves. Frequency is determined by the source and remains constant as waves cross boundaries between different media. When a continuous wave enters string 2 where the wave speed is smaller, the wavelength decreases (from v = fλ) but the frequency stays the same. The boundary cannot create or destroy wave cycles; it must transmit them at the same rate they arrive. Choice A incorrectly assumes frequency depends on wave speed, confusing medium-dependent properties (speed, wavelength) with source-dependent properties (frequency). Remember that frequency is always conserved across boundaries between media.
A longitudinal sound wave in air has frequency $440\ \text{Hz}$ and speed $343\ \text{m/s}$ . The sound enters a region of warmer air where the speed is higher, but the source remains the same. Which statement best describes the sound wave in warmer air?
Answer: The frequency is unchanged and the wavelength increases. This question tests understanding of properties of wave pulses and waves. Sound waves travel faster in warmer air because the molecules move faster, increasing the speed of sound. When sound waves enter a new medium, the frequency remains constant at 440 Hz because it's determined by the source—the source continues vibrating at the same rate. Using v = fλ, if wave speed v increases (in warmer air) and frequency f stays constant, then wavelength λ must increase proportionally. This is analogous to water waves entering deeper water. Choice A incorrectly claims frequency increases and wavelength decreases, misunderstanding that frequency is locked to the source. Remember: when waves change media, frequency stays constant while speed and wavelength change in the same direction.
A wave pulse moves to the right on a rope. The rope is replaced by an identical rope, but the tension is increased by a factor of 4. Which statement best describes the pulse speed?
Answer: It doubles because wave speed on a string scales as $\sqrt{T}$ . This question tests understanding of properties of wave pulses and waves. Wave speed on a string is given by v = √(T/μ), where T is tension and μ is linear mass density. When tension increases by a factor of 4, the new speed becomes v_new = √(4T/μ) = 2√(T/μ) = 2v, so the speed doubles. Choice B incorrectly assumes direct proportionality between speed and tension, reflecting the misconception that wave speed scales linearly with tension rather than with the square root of tension. Remember that wave speed on a string varies as the square root of tension.
A sinusoidal wave on a string has speed $12\ \text{m/s}$ and wavelength $3.0\ \text{m}$ . The amplitude is doubled while the string and tension remain unchanged. Which quantity changes for the wave?
Answer: Only the energy transported increases. This question tests understanding of properties of wave pulses and waves. Wave speed on a string depends only on the medium properties (tension and linear mass density), not on amplitude, frequency, or wavelength. Since the string and tension remain unchanged, the wave speed stays at 12 m/s regardless of amplitude changes. The frequency f = v/λ = 12/3 = 4 Hz also remains constant because both speed and wavelength are unchanged. However, wave energy is proportional to the square of amplitude (E ∝ A²), so doubling the amplitude quadruples the energy transported by the wave. Choice B incorrectly assumes amplitude affects wave speed, conflating wave properties with energy transport. Remember: amplitude affects energy but not speed, frequency, or wavelength.
A wave has speed $v$ in a medium. If its frequency is tripled while the medium is unchanged, which statement best describes the wavelength?
Answer: It becomes one-third as large because $\lambda=v/f$ . This question tests understanding of properties of wave pulses and waves. The wave equation v = fλ can be rearranged to λ = v/f, showing that wavelength is inversely proportional to frequency when wave speed is constant. Since the medium is unchanged, the wave speed v remains constant. When frequency is tripled (f → 3f), the wavelength becomes λ = v/(3f) = (1/3)(v/f), or one-third of its original value. Choice A incorrectly assumes direct proportionality between wavelength and frequency, which would violate the wave equation. When frequency changes but the medium stays the same, wavelength must change inversely to maintain constant wave speed.
A longitudinal sound wave travels through air at constant speed. If the amplitude of the pressure variation is decreased, which statement best describes the wave's speed?
Answer: It remains the same because speed depends on the medium, not amplitude. This question tests understanding of properties of wave pulses and waves. The speed of sound in air depends on the medium's properties—specifically temperature, pressure, and composition—not on the wave's amplitude or intensity. Sound speed in air at room temperature is approximately 343 m/s regardless of whether the sound is loud (large amplitude) or quiet (small amplitude). Amplitude affects the energy carried by the wave and the loudness we perceive, but not the wave's propagation speed. All sound waves, from whispers to explosions, travel at the same speed through the same air conditions. Choice A incorrectly links amplitude to wave speed, confusing energy content with propagation velocity, a common misconception. Remember: wave speed is set by the medium's properties, while amplitude affects only the energy transported.
A wave pulse travels on a long spring. The pulse is created with twice the initial amplitude while the spring and tension are unchanged. Which statement best describes the pulse speed?
Answer: It is unchanged because speed depends on the medium, not amplitude. This question tests understanding of properties of wave pulses and waves. Wave speed in a medium depends only on the medium's properties (like tension and mass density for a spring), not on the wave's amplitude. Doubling the amplitude increases the energy carried by the pulse but doesn't affect how fast it propagates through the spring. Choice A incorrectly suggests larger amplitude pulses travel faster, reflecting the misconception that wave characteristics like amplitude influence propagation speed. Remember that wave speed is a property of the medium, independent of wave amplitude or energy.
A transverse wave on a rope travels at constant speed $v$ in the same rope. If the driving frequency doubles while tension is unchanged, which statement best describes the new wavelength?
Answer: It becomes half as large because the wave speed stays the same. This question tests understanding of properties of wave pulses and waves. For waves on a rope, the wave speed v is determined by the rope's tension and linear mass density, not by the frequency or amplitude of the wave. The fundamental wave relationship is v = fλ, where v is wave speed, f is frequency, and λ is wavelength. Since the rope and tension are unchanged, the wave speed v remains constant. When frequency doubles (f → 2f) and speed stays the same, the wavelength must become half as large (λ → λ/2) to maintain the relationship v = fλ. Choice A incorrectly assumes that wave speed depends on frequency, a common misconception that confuses the properties set by the medium with those set by the source. Remember: wave speed is a property of the medium, while frequency is set by the source.
A sinusoidal wave on a string has frequency $5.0\,\text{Hz}$ and wavelength $0.40\,\text{m}$ . The string is replaced with one where waves travel twice as fast. Which quantity changes when the same driver continues oscillating?
Answer: The wavelength doubles while the frequency stays the same. This question tests understanding of properties of wave pulses and waves. The wave relationship v = fλ connects wave speed, frequency, and wavelength. When the string is replaced with one where waves travel twice as fast, the wave speed doubles from 2.0 m/s to 4.0 m/s. Since the same driver continues oscillating, the frequency remains 5.0 Hz (the source determines frequency). To maintain v = fλ with doubled speed and constant frequency, the wavelength must double from 0.40 m to 0.80 m. Choice A incorrectly assumes frequency changes, reflecting the misconception that frequency depends on the medium rather than the source. Always remember that frequency is set by the source, while wavelength adjusts based on the medium's wave speed.
A pulse on a rope carries energy $E$ . The amplitude is tripled while the rope tension and linear density stay the same. Which statement best describes the energy carried?
Answer: It becomes $9E$ because energy is proportional to amplitude squared. This question tests understanding of properties of wave pulses and waves. The energy carried by a wave pulse is proportional to the square of its amplitude: E ∝ A². This relationship holds for all mechanical waves because energy is stored in the displacement from equilibrium, and both kinetic and potential energy scale with displacement squared. When amplitude is tripled (A → 3A), the energy becomes E → 9E because (3A)² = 9A². The rope's tension and density determine the wave speed but don't change the amplitude-energy relationship. Choice A incorrectly assumes a linear relationship between amplitude and energy, missing the quadratic dependence that arises from the physics of oscillatory motion. Remember: wave energy is proportional to amplitude squared (E ∝ A²), making amplitude changes have dramatic effects on energy transport.
A water wave travels from deep water into shallower water. The source continues producing waves at the same frequency. Which statement best describes what happens to the wavelength in the shallow region?
Answer: It decreases because the wave speed decreases. This question tests understanding of properties of wave pulses and waves. Water waves travel slower in shallow water than in deep water due to interaction with the bottom. When waves cross from one medium to another, frequency remains constant because it's determined by the source—the source continues producing waves at the same rate. Using the wave equation v = fλ, if wave speed v decreases and frequency f stays constant, then wavelength λ must decrease proportionally. This is why ocean waves appear to bunch up as they approach shore. Choice D incorrectly claims frequency changes in shallow water, misunderstanding that frequency is set by the source, not the medium. Remember: when waves change media, frequency stays constant while speed and wavelength change together.
A transverse wave travels along a taut string with speed $v=12\ \text{m/s}$ . The string is replaced with another string under the same tension but with twice the linear mass density. Which statement best describes the wave speed in the new string?
Answer: It is $\dfrac{12}{\sqrt{2}}\ \text{m/s}$ because wave speed scales as $1/\sqrt{\mu}$ . This question tests understanding of properties of wave pulses and waves. The speed of a transverse wave on a string is given by v = √(T/μ), where T is tension and μ is linear mass density. When the linear mass density doubles while tension remains constant, the wave speed becomes v_new = √(T/2μ) = √(1/2) × √(T/μ) = v/√2 = 12/√2 m/s. Choice C incorrectly assumes wave speed depends on source frequency, reflecting the misconception that the source controls wave speed rather than the medium. Remember that wave speed in a medium is determined solely by the medium's properties, not by the source characteristics.
A sinusoidal wave on a string has frequency $10\ \text{Hz}$ and speed $20\ \text{m/s}$ . The string tension is increased so the wave speed becomes $30\ \text{m/s}$ while the driver frequency stays $10\ \text{Hz}$ . Which quantity changes?
Answer: The wavelength increases to $3.0\ \text{m}$ . This question tests understanding of properties of wave pulses and waves. Initially, the wave has f = 10 Hz and v = 20 m/s, giving wavelength λ = v/f = 20/10 = 2.0 m. When tension increases, wave speed on the string increases to 30 m/s because v = √(T/μ). The driver continues at 10 Hz, so frequency remains unchanged—frequency is always determined by the source. Using v = fλ with the new speed: λ = 30/10 = 3.0 m. The wavelength increases from 2.0 m to 3.0 m to accommodate the higher speed at the same frequency. Choice A incorrectly assumes frequency changes with tension, confusing medium properties with source properties. Remember: changing the medium affects speed and wavelength, but frequency is locked to the source.
A continuous wave travels along a string with wavelength $\lambda=0.60\,\text{m}$ and speed $v=9.0\,\text{m/s}$ . The string tension is adjusted so the wave speed becomes $6.0\,\text{m/s}$ while the driver frequency stays constant. Which statement best describes the new wavelength?
Answer: It becomes $0.40\,\text{m}$ because wavelength is proportional to wave speed at fixed frequency. This question tests understanding of properties of wave pulses and waves. The wave relationship v = fλ governs how wavelength changes when wave speed changes. Initially, the frequency is f = v/λ = 9.0/0.60 = 15 Hz. When tension is adjusted to reduce wave speed to 6.0 m/s while the driver frequency remains constant at 15 Hz, the new wavelength becomes λ = v/f = 6.0/15 = 0.40 m. Choice C incorrectly assumes wavelength depends only on amplitude, confusing wave propagation properties with wave energy. Always use v = fλ to relate changes in wave speed, frequency, and wavelength.
Two waves travel in the same rope under the same tension: Wave 1 has frequency $f$ and Wave 2 has frequency $2f$ . Which statement best compares their speeds?
Answer: They have equal speed because the medium determines wave speed. This question tests understanding of properties of wave pulses and waves. Wave speed in a rope depends only on the rope's physical properties: tension T and linear mass density μ, according to v = √(T/μ). Since both waves travel in the same rope under the same tension, they experience identical medium conditions and therefore have the same speed. The frequency of a wave is set by the source and doesn't affect how fast the wave propagates through the medium. Wave 2 has twice the frequency of Wave 1, which means it has half the wavelength (since v = fλ and v is constant), but both waves travel at the same speed. Choice A incorrectly assumes higher frequency waves travel faster, confusing the rate of oscillation with the rate of propagation. Remember: all waves in the same medium under the same conditions travel at the same speed, regardless of their frequency or amplitude.
A wave on a string has amplitude $A$ and wavelength $λ$ . The amplitude is doubled while the string and driving frequency stay the same. Which quantity changes?
Answer: Energy transported, because it increases with amplitude. This question tests understanding of properties of wave pulses and waves. Wave amplitude represents the maximum displacement from equilibrium and is independent of the wave's speed, frequency, or wavelength for mechanical waves on strings. The wave speed on a string depends only on the string's tension and linear mass density, not on amplitude. Since the string properties and driving frequency remain unchanged, the wavelength (λ = v/f) also stays constant. However, the energy transported by a wave is proportional to the square of its amplitude (E ∝ A²), so doubling the amplitude quadruples the energy transported. Choice A incorrectly assumes amplitude affects wave speed, a misconception that confuses energy content with propagation speed. Remember: amplitude affects energy transport but not the kinematic properties (v, f, λ) of the wave.
A periodic wave on a rope has frequency $f=5.0\ \text{Hz}$ and wavelength $\lambda=0.80\ \text{m}$ . The rope tension is increased so the wave speed doubles while the source frequency stays constant. Which quantity changes?
Answer: The wavelength doubles. This question tests understanding of properties of wave pulses and waves. The wave equation v = fλ relates wave speed, frequency, and wavelength. When tension increases and wave speed doubles from 4.0 m/s to 8.0 m/s while the source maintains constant frequency at 5.0 Hz, the wavelength must change to satisfy the wave equation: λ_new = v_new/f = 8.0/5.0 = 1.6 m, which is double the original 0.80 m. Choice B incorrectly suggests frequency doubles, reflecting the misconception that changing the medium properties affects the source frequency. Remember that the source controls frequency, while wavelength adjusts to maintain v = fλ when wave speed changes.
A periodic wave on a string has period $T=0.25\ \text{s}$ . Which statement best describes its frequency?
Answer: It is $4.0\ \text{Hz}$ because $f=1/T$ . This question tests understanding of properties of wave pulses and waves. Frequency and period are reciprocals of each other, related by f = 1/T. With a period of 0.25 s, the frequency is f = 1/0.25 s = 4.0 Hz. This means the wave completes 4 full oscillations every second. Frequency is a property of the source and remains constant even when the wave enters a different medium—only wavelength adjusts to accommodate the new wave speed. Choice C incorrectly suggests frequency would change in a slower medium, confusing it with wavelength changes. When given period, always use f = 1/T to find frequency, ensuring your units are consistent (s⁻¹ = Hz).
A sinusoidal wave on a string has displacement amplitude $A$ and angular frequency $\omega$ . The amplitude is doubled while $\omega$ and the medium are unchanged. Which statement best describes the maximum transverse speed of a point on the string?
Answer: It doubles because $v_{\max}$ is proportional to amplitude for fixed $\omega$ . This question tests understanding of properties of wave pulses and waves. For a sinusoidal wave, the maximum transverse speed of a point on the string is vmax = Aω, where A is amplitude and ω is angular frequency. This represents how fast the string moves perpendicular to the wave direction, not the wave speed along the string. When amplitude doubles while ω remains constant, the maximum transverse speed also doubles. Choice C confuses transverse particle motion with longitudinal wave propagation speed, a common misconception. Remember to distinguish between wave speed (horizontal propagation) and particle speed (vertical oscillation).
Two waves travel in different media. Wave 1 has speed $v_1$ and frequency $f_1$ ; wave 2 has speed $2v_1$ and the same frequency $f_1$ . Which statement best describes the wavelengths?
Answer: $\lambda_2=2\lambda_1$ because $\lambda=v/f$ at fixed frequency. This question tests understanding of properties of wave pulses and waves. The fundamental relationship v = fλ shows that at constant frequency, wavelength is directly proportional to wave speed. Since wave 2 has twice the speed of wave 1 but the same frequency, its wavelength must be twice as large: λ₂ = v₂/f = 2v₁/f = 2(v₁/f) = 2λ₁. Choice A incorrectly suggests higher speed means shorter wavelength, reflecting the misconception that speed and wavelength are inversely related. Remember that at fixed frequency, wavelength scales directly with wave speed.

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