A. It is said that Galileo discovered a basic principle of the pendulum - that t

Question

A. It is said that Galileo discovered a basic principle of the pendulum - that the period is independent of the amplitude - by using his pulse to time the period of swinging lamps in the cathedral as they swayed in the breeze. Suppose that one oscillation of a swinging lamp takes 4.9 seconds. How long is the lamp chain? m

B. A sinusoidal wave has a period of 0.95 s and wavelength 2.4 m. What is the wave speed? m/s

C. A violin string is 45 cm long. It sounds the musical note A (440 Hz) when played without fingering. How far from the end of the string should you place your finger to play the note C (523 Hz)? cm

Explanation / Answer

Here ,

A)

let the length of keychain is L

as T = 2pi * sqrt(L/g)

4.9 = 2pi * sqrt(L/9.8)

solving for L

L = 5.96 m

the length of key chain is 5.96 m

B)

T = 0.95 s

wavelength = 2.4 m

speed of wave = wavelength/T

speed of wave = 2.4/.95 m/s

speed of wave = 2.52 m/s

C)

let the finger should be placed at x cm from the left end

f1/f2 = L2/L1

440/523 = (45 - x)/45

solving for x

x = 7.142 cm

the finger should be placed at 7.142 cm from the end

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