A continuous succession of sinusoidal wave pulses are produced at one end of a v

Question

A continuous succession of sinusoidal wave pulses are produced at one end of a very long string and travel along the length of the string. The wave has frequency 61.0Hz , amplitude 4.55mm, and wavelength 0.600m . Part A How long does it take the wave to travel a distance of 8.00m along the length of the string? Part B How long does it take a point on the string to travel a distance of 8.00m , once the wave train has reached the point and set it into motion? Part C In parts (a) and (b), how does the time change if the amplitude is doubled? Express your answers numerically separated by a comma.

Explanation / Answer

Speed = wavelength x frequency = 0.600 x 61 = 36.6 m/s

Time = distance/speed = 8.00 / 36.6 = 0.219 s

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Distance per cycle moved by a point oscillating sinusoidally = 4 x 4.55 = 18.2 mm = 0.0182 m

Number of cycles = 8.00 / 0.0182 = 440 cycles

Period = 1/f = 1/61 = 0.016 s

Time = 440 x 0.016

= 7.04 s

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