An orchestra is rehearsing in an auditorium whose parallel rear walls are 10.0m apart. A tuning fork vibrates at a fixed frequency of 512Hz. During the morning rehearsal the air temperature in the hall is 15∘C; by the evening rehearsal it has risen to 25∘C. Assume the air is dry and still.
(a) Determine the speed of sound in air at each of the two temperatures, using the empirical relation v=331m/s+0.60m/s×T(∘C).
(b) For each temperature, calculate the wavelength of the sound produced by the tuning fork.
(c) Find the percentage change in wavelength between the morning and evening rehearsals.
(d) Standing waves form between the rear walls when integer half-wavelengths fit exactly into the 10.0m separation. For the first three possible standing-wave modes, describe qualitatively how the positions of nodes and antinodes shift between morning and evening.