(11%) Problem 17: You have been hired by a professional musician as an interior designer. Your task is to design a very special enclosed rectangular glass shower stall. The specications are based on which notes, when sung in the shower, will resonate. Your 19 meter tall client takes showers so that the air temperature is Thor = 316C .Your client wants the shower stall to resonate precisely at f; = 169 Hz,f2 = I85 Hz, and f3 = 396 Hz. Note that the stall is to be wider than it is deep, and that no dimension of the shower stall can be less than 50 cm. Assume that each dimension of the shower works like a resonance tube that is closed on both ends. _ 20 9'0 Part (a) Calculate the speed of sound 1n air v5 (in nus), while your client is showering Recall that the speed of sound 1n air (in mls) can be found using VB : 331.5 1/(1 + [372731.150 where Tis the air temperature in C. v5 = 350.72 rs = 350.? if Correct! _ 20 (it; Part (D) How tall (in meters) should the shower stall be if it is to resonate at the lowest frequency and your client can stand up fully while showering? h = 2.080 I/ Correct! 8 20 2% Part (1:) Calculate the minimum depth (in meters) of the shower stall. Grade Summary d = 0948' Deductions Potential 100% Submissions Attempts remaining: (_ per attempt) l-\" cycled 2 vcgms o Radius II_- 3 4 Submit | l I give up! Hints: _ for a deduction. Hints remaining: _ Feedback: _ for a deduction -Use the frequency to calculate the wavelength of the sound. No meaningful feedback available for the current submission. -How much of the wave could t in the shower stall given your boundary conditions? Perhaps a sketch will help. -Since the depth is the smallest of the 3 dimensions of the stall. you need to use the note with the shortest wavelength in your calculations. -If you design the shower to resonate at HZ wavelength, it will be less than 0.5 In wide. _ 8 20 9E! Part ((1) Calculate the minimum width (in meters) of the shower stall H = 0.4480 3' .\\ltcmp11- Remain - a 20% Part (e) At these frequencies trained musicians can generally distinguish 2 notes whose ratio is larger than 1.00579 (10 cents) If your client decides to take a shower that is 10C colder than that specied, what 1s the ratio of the hot to the cold resonant frequencies