1. (15%) A 0.50 m rope is attached to a vibrator of adjustable frequency. The waves produced by the vibrator travel down

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1. (15%) A 0.50 m rope is attached to a vibrator of adjustable
frequency. The waves
produced by the vibrator travel down the string and reflect off the
fixed end on the pulley. The
rope, which has a linear mass density of 0.006 kg/m, passes over a
pulley without
friction of a negligible mass, and the tension is provided by a
hanging mass of
1.0kg.
(a) (5%) Calculate the wavelength of the fundamental mode and
fourth normal mode
of standing waves.
(b) (10%) Calculate the frequencies in Hz to which the string
vibrator must be adjusted.
to produce the third and fifth normal modes of vibration of
standing waves.
Draw a diagram of this case and label each standing wave with
its
frequency.