mkania
Oct5-05, 09:03 PM
Okay, here is my approach. Let me know if you think it makes sense.
We have c = f\lambda and c = \sqrt{(\gamma RT)/M} . In the fundamendal mode, \lambda = 2L. So
2f_\mathrm{He}L = \sqrt{(\gamma_\mathrm{He}RT)/M_\mathrm{He}} (1)
and
2fL = \sqrt{(\gamma_\mathrm{air}RT)/M_\mathrm{air}} (2)
Dividing (1) by (2),
f_\mathrm{He}/f = \sqrt{(\gamma_\mathrm{He}M_\mathrm{air})/(\gamma_\mathrm{air}M_\mathrm{He})}
so
f_\mathrm{He} = f\sqrt{(\gamma_\mathrm{He}M_\mathrm{air})/(\gamma_\mathrm{air}M_\mathrm{He})}
We have c = f\lambda and c = \sqrt{(\gamma RT)/M} . In the fundamendal mode, \lambda = 2L. So
2f_\mathrm{He}L = \sqrt{(\gamma_\mathrm{He}RT)/M_\mathrm{He}} (1)
and
2fL = \sqrt{(\gamma_\mathrm{air}RT)/M_\mathrm{air}} (2)
Dividing (1) by (2),
f_\mathrm{He}/f = \sqrt{(\gamma_\mathrm{He}M_\mathrm{air})/(\gamma_\mathrm{air}M_\mathrm{He})}
so
f_\mathrm{He} = f\sqrt{(\gamma_\mathrm{He}M_\mathrm{air})/(\gamma_\mathrm{air}M_\mathrm{He})}