# Nodes and Antinodes

## Homework Statement

Consider the standing wave: 0.005sin(30x)cos(420t) m. Locate the antinode closest to x=0.25 m.

## The Attempt at a Solution

I'm not really sure how to tackle this problem except that i know that antinodes occur at the crests of the standing wave and that the distance between antinodes is lamda/2. In the answers it says that: kXn=(2n+1)pi/2..... Xn=(2n+1)pi/(2k) and when you plug in n=2 it is 0.261 m...does anyone know how they got the initial formula?

## Answers and Replies

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Doc Al
Mentor
Consider the spatial factor sin(kx). What values of x give the maximum amplitude?

Consider the spatial factor sin(kx). What values of x give the maximum amplitude?
aren't they pi/2, 3pi/2, 5pi/2, 7pi/2...etc?

Doc Al
Mentor
aren't they pi/2, 3pi/2, 5pi/2, 7pi/2...etc?
Good. But that's the value for kx, not x. (In this problem, k = 30.) How would you write that series using n, where n = 0, 1, 2, and so on? Compare that to the formula given.