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Bill is making waves on a rope with one end attached to a wall. When he starts moving the rope quickly, the frequency of the waves created on the rope doubles. What happens to the energy that is transferred to the wall when the frequency of the waves doubles?
A.
The energy transferred to the wall is tripled.
B.
The energy transferred to the wall is doubled.
C.
The energy transferred to the wall is halved.
D.
The energy transferred to the wall is quadrupled.
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Answered by
GPT-5 mini
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D. Quadrupled.
Reason: The average power (energy per second) carried by a transverse wave on a string is
P = (1/2) μ ω^2 A^2 v,
with ω = 2πf. So P ∝ ω^2 ∝ f^2 (for fixed amplitude A and wave speed v). If f doubles, P increases by 2^2 = 4, i.e. the energy transferred to the wall per unit time is quadrupled.
Reason: The average power (energy per second) carried by a transverse wave on a string is
P = (1/2) μ ω^2 A^2 v,
with ω = 2πf. So P ∝ ω^2 ∝ f^2 (for fixed amplitude A and wave speed v). If f doubles, P increases by 2^2 = 4, i.e. the energy transferred to the wall per unit time is quadrupled.
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