2. A string with length L = 0.80 m and linear density µ = 2.5 g/m is under tensi

Question

2. A string with length L = 0.80 m and linear density µ = 2.5 g/m is under tension
F = 4.0 N. The string is fixed at each end and when driven at the frequency of the n = 3
harmonic, a standing wave with amplitude A = 0.50 cm is produced. The standing wave
is composed to two component waves y1(x, t) and y2(x, t).
(a) Find the amplitudes of the component waves.
(b) Find the angular frequencies of the component waves.
(c) Find the wave numbers of the component waves.
(d) Find the wave speeds of the component waves.
(e) Find the maximum particle velocity of the component waves.

Explanation / Answer

a) A/2 = 0.25cm. b) wave velocity v=sqrt(T/linear density)=40(m/s). lamda=0.8*2/3=1.6/3. f=v/lamda=75(Hz) c) two wave. d) its 40m/s e) w=2pif=150pi(rad/s). maximum speed v=w*A=235(cm/s)

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