Question

Cousin Throcky holds one end of the string and wiggles it up and down sinusoidally with frequency 2.00 Hz and amplitude 0.075 m. The wave speed on the string is 12 m/s. At t = 0 s, Throcky’s end has maximum positive displacement and is instantaneously at rest. Assume the wave travels to the right and no wave bounces back from the far end.

(vi)Derive an equation for maximum transverse velocity. Calculate the value. (3 marks) (vii)At what maximum power does Throcky put energy into the string? The mass per unit length of string is 0.25 kg/m and Throcky applies tension 36.0 N. (3 marks) (viii) What is the average power when the amplitude is 7.50 mm? (3 marks)

Answer 1

= 2 HZ The amplitude A of the wave is just the amplitude of maken to A = 0.075 m 12 mis of the end of clothesline, A=0.075m. of Similarly the frequency of the clothesline. W=2 Tlf (277 * 2) = Time period is T = is f= 2 HZ of the end 12.6 rad /second. 1 =0.5 second I! f ง 12 6 m. Wavelength x= 2 f we find the wave number (K) 2T 1.05 roolm K = 2T . we can write down the were function as :- (e - - 2T (26 y (x, t)= A las 27 -0.075 los 2T/x t os )

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Vi o Mascimum transverre F= 36 N M = 0.25kg/m 12 m/s v= JE JE 36 0:23 v=12m is (0.075) vii) Pmas = JuF W² A = Jo. 25x36 * (12.6)²X Pmarc = 2.66W Wild I up w² A² Paverage 1. 33 W Por = I x 2.66 = 2 Pav 1.33W 0.0075 m vili) when Anar 7.5mm 8 A new = (lxa > Pao 1:33 lloj? en33 0.0 133 Watt. Pao 13.3 mW