An observant fan at a baseball game notices that the radio commentators have low

Question

An observant fan at a baseball game notices that the radio commentators have lowered a microphone from their booth to just a few inches above the ground, as shown in the figure (Figure 1). The microphone is used to pick up sound from the field and from the fans. The fan also notices that the microphone is slowly swinging back and forth like a simple pendulum. Using her digital watch, she finds that 13 complete oscillations take 55.0 s. How high above the field is the radio booth? (Assume the microphone and its cord can be treated as a simple pendulum.) h = m

Explanation / Answer

As

Time period, T = 55/13 s

Since for a simple pendulum

T =2 (h/g)1/2

That means

2 (h/g)1/2 = 55/13

(h/g)1/2 = (55/13)(1/2)

(h/g) = {(55/13)(1/2)}2

h = {(55/13)(1/2)}2g

h = 4.448 meter

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