A \(600\,\mathrm{Hz}\) source is stationary in air. A listener moves toward it at \(20\,\mathrm{m\,s^{-1}}\). Use \(v=340\,\mathrm{m\,s^{-1}}\) to find the heard frequency.

A \(600\,\mathrm{Hz}\) source moves toward a stationary listener at \(20\,\mathrm{m\,s^{-1}}\). Use \(v=340\,\mathrm{m\,s^{-1}}\) to find the heard frequency.

A source and listener move away from each other. Is the heard frequency higher or lower than the source frequency?

A listener moves away from a stationary \(500\,\mathrm{Hz}\) source at \(10\,\mathrm{m\,s^{-1}}\). Use \(v=340\,\mathrm{m\,s^{-1}}\) to find the heard frequency.

A stationary listener hears a \(1000\,\mathrm{Hz}\) source moving away at \(30\,\mathrm{m\,s^{-1}}\). Use \(v=340\,\mathrm{m\,s^{-1}}\) to find the heard frequency.

A \(700\,\mathrm{Hz}\) source is stationary. A listener moves toward it at \(15\,\mathrm{m\,s^{-1}}\). Use \(v=345\,\mathrm{m\,s^{-1}}\).

A \(700\,\mathrm{Hz}\) source moves toward a stationary listener at \(15\,\mathrm{m\,s^{-1}}\). Use \(v=345\,\mathrm{m\,s^{-1}}\).

A source emits \(450\,\mathrm{Hz}\). The listener moves toward the source at \(12\,\mathrm{m\,s^{-1}}\), and the source moves toward the listener at \(18\,\mathrm{m\,s^{-1}}\). Use \(v=340\,\mathrm{m\,s^{-1}}\).

A source emits \(450\,\mathrm{Hz}\). The listener moves away from the source at \(12\,\mathrm{m\,s^{-1}}\), and the source moves away from the listener at \(18\,\mathrm{m\,s^{-1}}\). Use \(v=340\,\mathrm{m\,s^{-1}}\).

A stationary listener hears \(880\,\mathrm{Hz}\) from a source whose emitted frequency is \(800\,\mathrm{Hz}\). The source is moving toward the listener. Use \(v=340\,\mathrm{m\,s^{-1}}\) to find the source speed.

A listener moving toward a stationary source hears \(660\,\mathrm{Hz}\) from a \(600\,\mathrm{Hz}\) source. Use \(v=340\,\mathrm{m\,s^{-1}}\) to find the listener speed.

A car horn emits \(500\,\mathrm{Hz}\). A stationary observer hears \(540\,\mathrm{Hz}\) as the car approaches and \(465\,\mathrm{Hz}\) as it recedes. Are these values consistent with one car speed under the simple Doppler model? Use \(v=340\,\mathrm{m\,s^{-1}}\).

Explain why the source speed appears in the denominator of the Doppler formula, while listener speed appears in the numerator.

A source and listener move together through still air at the same speed in the same direction, with the source behind the listener. Does the listener hear a Doppler shift? Use the combined formula to justify.

For a stationary listener and a moving source, derive \(f_L=f_Sv/(v-v_S)\) from the changed wavelength ahead of the source.

For a stationary source and moving listener, derive \(f_L=f_S(v+v_L)/v\) from the listener meeting wavefronts at a changed rate.

A source moves toward a wall at speed \(u\) and emits frequency \(f_S\). The wall is stationary and reflects the sound. Derive the frequency of the echo heard back at the moving source, assuming \(u<v\).

A listener at rest hears frequency \(f_+\) as a source approaches and \(f_-\) as the same source recedes at the same speed. Derive the source speed \(u\) in terms of \(f_+\), \(f_-\), and \(v\).

Using \(f_L=f_S(v+v_L)/(v-v_S)\), derive the first-order fractional shift for speeds much smaller than \(v\). Keep terms only to first order in \(v_L/v\) and \(v_S/v\).

A wind blows from source to listener at speed \(w\). A source and listener are both at rest relative to the ground. Explain whether the listener hears a Doppler shift, and distinguish changed wave speed relative to ground from changed emission frequency.