# How would red (frequency) shift work for sound waves on the surface of a balloon?

Imagine an expanding balloon with a source of vibrations, in the fabric of the balloon, on one side (pole), and a microphone on the other side (pole). We would expect the sound to be 'red shifted' that is the microphone would detect sound at a lower pitch, longer wavelength, than it was emitted. But why? There could be a Doppler effect but the velocity of the emitted sound waves is at right angles to the velocity of the expansion, so do we expect a Doppler effect?

There is likely to be a frequency shift due to the increasing size of the balloon. If the balloon doubles in size you might expect the wavelength of the sound in the balloon skin to double. So would the frequency shift be a function of the speed of expansion or the size of the balloon when the signal was received, relative to when it was emitted, or some combination of the two?

Of course the speed of the sound within the balloon skin may alter as the skin stretches, also giving a frequency shift. This could be measured by comparing the speed of the sound, or the shift in frequency, for the static balloon at different sizes. Might this be very loosely analogous to gravitational red shift?

Ideally the microphone should only respond to vibrations in the balloon skin, not the surrounding air. With a bit of luck, the microphone might be able to pick up vibrations that have travelled 0.5, 1.5, 2.5 etc times around the balloon, increasing the sensitivity of the experiment.

The answers to this experiment, thought or actual, could have implications for cosmology.