A hand holding a rope moves up and down to create a transverse wave on the rope.

Question

A hand holding a rope moves up and down to create a transverse wave on the rope. The hand completes an oscillation in 3 s, and the wave travels along the string at 0.5 m/s. The amplitude of the wave is 0.05 m.

a.) Find the frequency at which the crests pass a given point in space.
0.33  Hz
(this answer is correct)
b.) Find the distance between two adjacent crests on the wave.
1.51  m
(this is correct)
c.) There is a blue spot drawn onto the rope with a pen. Find the distance this spot travels in one period.
  1.51m (this was incorrect).

I thought c) was 1.51m but that was incorrect. Does anybody know how to solve this correctly? Thanks

__________________

Part D)

A nylon guitar string has a linear density of 7.2 g/m and is under a tension of 152 N. The fixed supports are 90 cm apart. The string is oscillating in the standing wave pattern shown below.

The speed is 145m/s

(d) find the wavelength in____  cm

The answer is not 0.6cm

Explanation / Answer

a) frequency = 1/T = 1 / 3 = 0.33 Hz

b) distance between twi adjacent crest = wavelength = v/f or vT

lambda = 0.5 x 3 = 1.5 m

c) 1.5 m is displacement of dot not distance traveled by dot.

distance will be = length of arc = 2piA = 2 x pi x 0.5 = 3.14 m

d) length of string L = 3 x wavelength / 2

90 = 1.5 x wavelength

wavelength = 60 cm

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