Question

The distance between two successive crests of a certain transverse wave is 1.15 m. 20 crests pass a given point along the direction of travel every 16.2 s. What is the wave speed? Answer in units of m/s.

how do I do this?

Answer 1

`1.42"m/s"`

Explanation:

The distance between two successive crests of a wave is one way to define its wavelength, so `lambda=1.15"m"`.

The frequency of a wave is the number of waves passing a given point per second, so `f=20/16.2=1.23"Hz"`.

The speed of a wave is given* as `v=lambdaf`, so here `v=1.15*1.23=1.42"m/s"`

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*This is because the wavelength is the "distance per wave" and the frequency is the "number of waves per second," so multiplying the two gives "distance per second." This can be verified with dimensional analysis:
`"meters"/cancel"wave"timescancel"waves"/"second"="meters"/"second"`