this particular day I to be studying about waves. So, we learn the formula "speed = frequency * wavelength". Over there is a inquiry come the end in mine book

If the frequency the water tide is decreased, what will happened to the speed?

So, this is what did,

If rate = frequency * wavelengthThat method speed is directly proportional to frequencyWhen frequency increases, rate increases and also vice versa.

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Eventually, I compose the rate of the water waves will decrease. Yet the answer indigenous the publication is the speed of water waves will stay constant.

So, my concern is why the rate of water waves will certainly stay consistent if the frequency the water waves is decreased?

waves acoustics frequency rate
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edited Sep 27 "18 in ~ 5:02

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I will hold-up the use of water waves, fairly use tide on a string, as in case of water waves, nonlinear impacts can be over there which have the right to have different dispersion relations favor in the instance of shallow water/ deep water waves and thereby a different relation for group velocity 보다 you mentioned. So I will derive the case for tide on a string and also then map out the analogous instance for water waves, taking right into account appropriate approximations. So for waves on a string us have

$$c = u lambda$$

Now we know that the rate of the tide is dependence on the tension and the straight mass density.

$$c = sqrtT/mu$$ because neither of them are transforming in your example, we recognize that the rate of the tide is constant. Therefore from the an initial relation the just thing that changes with readjust with frequency is the wavelength and also not speed.

See more: What Does Lower Extreme Mean In Math, Lower Extreme

For water waves, similarly, using appropriate limits if the dispersion relation yields a similar group velocity relation through frequency and also wavelength, we have the right to say that due to the fact that the pressure and the density are not changed, and as a result, the only thing that alters with change with frequency is the wavelength and not speed.