A trombone is a brass instrument that can adjust its pitch by creating a longer or shorter chamber using a slide. If a trombone starts with a frequency of 845 hz, but then changes the size of the chamber to produce a sound wave that is half as long (1/2 the original wavelength), what is the new wavelength?
+33661 Wavelength is speed/frequency, so we need the speed of sound in air. If we assume dry air at sea level this is about 343 m/s. If original wavelength is L, then L=343/845m so new wavelength, Lnew is
$${\mathtt{Lnew}} = {\frac{{\mathtt{343}}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{845}}\right)}} \Rightarrow {\mathtt{Lnew}} = {\mathtt{0.202\: \!958\: \!579\: \!881\: \!656\: \!8}}$$ metres
or Lnew ≈ 0.203m
+33661 Wavelength is speed/frequency, so we need the speed of sound in air. If we assume dry air at sea level this is about 343 m/s. If original wavelength is L, then L=343/845m so new wavelength, Lnew is
$${\mathtt{Lnew}} = {\frac{{\mathtt{343}}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{845}}\right)}} \Rightarrow {\mathtt{Lnew}} = {\mathtt{0.202\: \!958\: \!579\: \!881\: \!656\: \!8}}$$ metres
or Lnew ≈ 0.203m
