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CrazyNeutrino
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Homework Statement
This is a problem from the Cambridge Natural Science Admissions Assesment.
A student carries out an experiment to measure the speed of sound. A loudspeaker that emits sound in all directions is placed between two buildings that are 128 m apart as shown. The student and loudspeaker are 48 m from one of the buildings.
The loudspeaker is connected to a signal generator that causes it to emit regular clicks. The student notices that each click results in two echoes, one from each building. The rate at which the clicks are produced is gradually increased from zero until each echo coincides with a new click being emitted by the loudspeaker.
What is the frequency of emission of clicks when this happens? (The speed of sound in air = 320 m/s)
Homework Equations
$$v=\frac{d}{t}$$
$$f=1/T$$
The Attempt at a Solution
The time taken between clicks must be equal to the time taken between the student hearing echoes at this frequency. ##t_1= \frac{96}{320}## and ##t_2=\frac{160}{320}##
$$T_{click} = t_2 - t_1 = \frac{64}{320} = \frac{1}{5}$$
$$F=\frac{1}{T}=5 Hz$$
The correct answer is 10 Hz. Why?
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