A wave travels along a stretched string. Is it transverse or longitudinal?

Sound travels through air as a sequence of compressions and rarefactions. Is this transverse or longitudinal?

A periodic wave has frequency \(15\,\mathrm{Hz}\) and wavelength \(0.40\,\mathrm{m}\). Find the wave speed.

A disturbance moves to the right while each element of the medium moves up and down. Classify the wave and explain the geometric reason in one sentence.

A compression wave in a spring has speed \(6.0\,\mathrm{m\,s^{-1}}\) and period \(0.20\,\mathrm{s}\). Find the spacing between successive compressions.

A student says, "If a marked particle in the medium is moving left at one instant, the wave must also be moving left." Explain why this conclusion is not valid.

Two waves travel along the \(+x\)-direction with the same \(\lambda\) and \(f\). In wave A the medium displacement is always along \(\hat y\). In wave B it is always along \(\hat x\). Compare their classifications and explain why equal \(\lambda\) and \(f\) do not force the same wave type.

A wave propagates along \(+x\) and the local displacement is \[ \vec \xi(x,t)=a\hat x\cos(kx-\omega t)+b\hat y\cos(kx-\omega t). \] Give the conditions on \(a\) and \(b\) for the wave to be purely longitudinal, purely transverse, or neither.