Daily Olympiad: Physics - Mechanical Waves Sound [20260512]

Challenge yourself with today's AP Physics practice! This test covers 'Mechanical Waves Sound' for Physics (AP Physics - 12). Level: Hard | Duration: 45 mins.

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1. A 1.2-meter-long string is tightened such that the left half has tension T and the right half has tension 4T. A standing wave pattern is formed with a node at the junction. What is the ratio of the frequencies of the harmonics formed in the left and right halves?

Solution
Correct: A
The frequency of a harmonic on a string is proportional to sqrt(T/μ), where μ is the linear mass density. Since the string is cut at the junction, μ is constant for both halves. The left segment has f₁ ∝ sqrt(T), and the right segment has f₂ ∝ sqrt(4T) = 2f₁. Hence, the ratio is 1:2.

2. A train moving at 30 m/s toward a stationary observer emits a 500 Hz whistle. If a wind of 10 m/s blows from the train toward the observer, what is the observed frequency?

Solution
Correct: A
Effective speed of sound becomes v' = 343 + 10 = 353 m/s. Observed frequency is f' = f(v' + vo)/(v' - vs) = 500(353)/(353 - 30) ≈ 548 Hz.

3. What is the speed of sound in a gas with molar mass 32 g/mol at 27°C? (γ = 1.4, R = 8.314 J/mol·K)

Solution
Correct: A
Use v = sqrt(γRT/M). Convert 27°C to 300 K and M to 0.032 kg/mol. v ≈ sqrt(1.4 * 8.314 * 300 / 0.032) ≈ 347 m/s.

4. A closed pipe produces a fundamental frequency of 125 Hz in air. If the speed of sound increases by 4%, what is the new fundamental frequency?

Solution
Correct: B
Fundamental frequency f = v/(4L). Since v increases by 4%, f increases by 4% → 125 * 1.04 = 130 Hz.