Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

If a water wave with length $ L $ moves with velocity $ v $ in a body of water with depth $ d, $ then$ v = \sqrt {\frac {gL}{2 \pi} \tanh (\frac {2 \pi d}{L}} $where $ g $ is the acceleration due to gravity. (See Figure 5.) Explain why the approximation$ v \approx \sqrt {\frac {gL}{2 \pi}} $ is appropriate in deep water.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$\sqrt{\frac{g L}{2 \pi}}$

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 11

Hyperbolic Functions

Derivatives

Differentiation

Campbell University

University of Michigan - Ann Arbor

University of Nottingham

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

02:09

If a water wave with lengt…

01:39

05:45

05:52

If a water wave with lengh…

Okay, we know that tan of two pi d over l We know we can write this as the limit as D approaches positive infinity of each of the four Pi di over Al to the minus one. This simplifies to the square root of G l over to pie. Now remember, that is the duct increases the function 10 h of two pied de over Al goes towards one though for the velocity as she out over too pie.

View More Answers From This Book

Find Another Textbook

Numerade Educator

02:55

If 2^a = 3^b = 6^c then show the relation between a,b and c

04:28

A woman has 60 notes in all rs.10 amd rs.20 of denomination .if the total wo…

01:16

if the number 7713A8 is divisible by 4, where A is a digit , what will be on…

02:34

the area of a rectangle is 54m square whose length is 3m more than its width…

00:44

the area of a square garden is 331.24 sq. metres. Find the length of railing…

03:08

a person wanted to distribute 96 apples and 112 oranges among the poor child…

03:06

Three children are walking . Their steps measure 36 cm , 72 cm and 90 cm . I…

00:52

If 80% of M is equal to 50% of N and N≠0, what is N/M equal to?

02:08

subtract the sum of (-100) and(-343) from the difference of (-345) and (-567…

02:33

Q. What is the smallest number by which 13068 should be divided, so that the…