Properties of Wave Pulses and Waves
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AP Physics 2 › Properties of Wave Pulses and Waves
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?
The period doubles.
The frequency doubles.
The wavelength doubles.
The amplitude doubles.
Explanation
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 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?
The amplitude halves because faster waves carry less energy.
The wavelength doubles while the frequency stays the same.
The frequency doubles while the wavelength stays the same.
Both frequency and wavelength stay the same because the driver is unchanged.
Explanation
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 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?
It is $24\ \text{m/s}$ because wave speed increases with mass density.
It is $\dfrac{12}{\sqrt{2}}\ \text{m/s}$ because wave speed scales as $1/\sqrt{\mu}$.
It is $12\ \text{m/s}$ because wave speed depends only on the source frequency.
It is $6\ \text{m/s}$ because wave speed decreases by a factor of 2.
Explanation
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 transverse wave on a string has speed $v=15\ \text{m/s}$ and wavelength $\lambda=0.60\ \text{m}$. The source frequency is increased so the frequency doubles while the string is unchanged. Which statement best describes the new wavelength?
It becomes $1.2\ \text{m}$ because wavelength is proportional to frequency.
It becomes $0.60\ \text{m}$ because wavelength depends only on amplitude.
It becomes $0.30\ \text{m}$ because wavelength is inversely proportional to frequency.
It becomes $0.15\ \text{m}$ because wave speed halves when frequency doubles.
Explanation
This question tests understanding of properties of wave pulses and waves. Using v = fλ, the initial frequency is f₁ = v/λ₁ = 15/0.60 = 25 Hz. When frequency doubles to f₂ = 50 Hz while the string properties (and thus wave speed) remain unchanged at 15 m/s, the new wavelength becomes λ₂ = v/f₂ = 15/50 = 0.30 m. Choice D incorrectly claims wave speed halves when frequency doubles, reflecting the misconception that changing source frequency affects the medium's wave speed. Remember that wave speed depends only on medium properties; when frequency changes, wavelength adjusts inversely to maintain constant speed.
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?
It quadruples because wave speed is directly proportional to tension.
It doubles because wave speed on a string scales as $\sqrt{T}$.
It is unchanged because tension affects only amplitude.
It halves because higher tension reduces oscillation of the rope.
Explanation
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 sound wave in air has frequency $440\ \text{Hz}$ and speed $343\ \text{m/s}$. The wave enters a region of warmer air where the speed becomes $360\ \text{m/s}$. Which statement best describes the wave in the warmer region?
Its speed stays the same while its amplitude decreases.
Its wavelength increases while its frequency stays the same.
Its frequency increases while its wavelength stays the same.
Its frequency decreases because the medium changed.
Explanation
This question tests understanding of properties of wave pulses and waves. When a wave crosses a boundary between media, its frequency remains constant because it's determined by the source, but wavelength changes to accommodate the new wave speed. Using v = fλ, the initial wavelength is λ₁ = 343/440 = 0.78 m, and in warmer air λ₂ = 360/440 = 0.82 m, showing wavelength increases. Choice D incorrectly claims frequency decreases when entering a new medium, reflecting the misconception that frequency depends on medium properties rather than being fixed by the source. Remember that frequency is invariant across boundaries while wavelength adjusts to the new wave speed.
A wave on a rope has amplitude $A$ and frequency $f$. The source is adjusted so the amplitude becomes $2A$ while $f$ and the rope remain the same. Which statement best describes the energy transported by the wave?
It becomes 4 times larger because energy is proportional to $A^2$.
It becomes 2 times larger because energy is proportional to amplitude.
It becomes 1/2 as large because larger amplitude reduces frequency.
It is unchanged because energy depends only on wave speed.
Explanation
This question tests understanding of properties of wave pulses and waves. The energy transported by a wave is proportional to the square of its amplitude (E ∝ A²) and also proportional to the square of frequency (E ∝ f²). Since frequency remains constant and amplitude doubles from A to 2A, the energy becomes proportional to (2A)² = 4A², making it 4 times larger. Choice A incorrectly assumes linear proportionality with amplitude, reflecting the misconception that wave energy scales directly with amplitude rather than with amplitude squared. Remember that wave energy depends on both amplitude squared and frequency squared.
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?
$\lambda_2=\tfrac{1}{2}\lambda_1$ because higher speed implies shorter wavelength.
$\lambda_2=2\lambda_1$ because $\lambda=v/f$ at fixed frequency.
$\lambda_2=4\lambda_1$ because doubling speed doubles frequency as well.
$\lambda_2=\lambda_1$ because wavelength depends only on amplitude.
Explanation
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.
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?
It decreases because energy is spread over a larger displacement.
It increases because larger amplitude pulses travel faster.
It is unchanged because speed depends on the medium, not amplitude.
It becomes zero because the spring must oscillate to transmit energy.
Explanation
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 sinusoidal wave in a slinky has wavelength $\lambda$ and amplitude $A$. The source is adjusted so the frequency increases while the slinky’s tension and mass density stay constant. Which statement best describes the wave speed?
It increases because higher frequency waves travel faster.
It becomes zero because energy transfer requires increasing amplitude.
It is unchanged because speed depends on the medium properties.
It decreases because shorter wavelength reduces speed.
Explanation
This question tests understanding of properties of wave pulses and waves. Wave speed in a medium like a slinky depends only on the medium's properties (tension and mass density), not on wave characteristics like frequency, wavelength, or amplitude. When frequency increases while the slinky's physical properties remain constant, the wave speed stays the same, though wavelength will decrease according to v = fλ. Choice A incorrectly suggests higher frequency waves travel faster, reflecting the misconception that wave characteristics affect propagation speed. Remember that wave speed is determined by the medium, not by the source or wave properties.