For a standing wave with wavelength \(0.80\,\mathrm{m}\), what is the spacing between neighboring nodes?

A string of length \(0.60\,\mathrm{m}\) supports waves at \(90\,\mathrm{m\,s^{-1}}\). Find the fundamental frequency.

For \(y(x,t)=2A\sin(kx)\cos(\omega t)\), state the condition for a node.

For \(y(x,t)=2A\sin(kx)\cos(\omega t)\), where are the antinodes?

A string fixed at both ends has length \(1.2\,\mathrm{m}\). What is the fundamental wavelength?

A standing wave on a string has wavelength \(1.0\,\mathrm{m}\). How many node intervals fit into a \(2.0\,\mathrm{m}\) length?

For \(y(x,t)=2A\sin(\pi x/L)\cos(\omega t)\), identify all node positions on the interval \(0\le x\le L\) and explain why this is the fundamental mode.

For the standing wave \(y(x,t)=2A\sin(kx)\cos(\omega t)\), find all positions in one wavelength interval where the oscillation amplitude is exactly \(A\).