Exercise 15.9 University Physics 13th Edition: A smoked glass plate was allowed

Question

Exercise 15.9 University Physics 13th Edition:

A smoked glass plate was allowed to have a free fall with its smoked side touching the vibrating stylus attached to one of the prongs of a fixed tuning fork. Sketch the wave pattern that would have been traced on the falling plate. If the difference between the lengths of two successive segments containing 3 waves each is 3.74 mm, determine the frequency 'f' of the tuning fork (g = 9.8 m/s^2)

ANSWER FROM TEXTBOOK: frequency = 153.57 Hz

HERE IS A LINK TO ALL THE NECESSARY EQUATIONS:   http://imgur.com/V6psLP4

Explanation / Answer

Here i am not getting how your answer is correct because as per i understood is that since in 3.74 mm there are 3 waves so wavelength will be 3.74/3 = 1.25 mm

And then since frequency *wavelength = speed of wave

So either you need to provide speed of wave or it can be considered as speed of light but then answer won't be same as per given by you.

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