A string of length 0.90 m, fixed at both ends, has its first two resonant frequencies at 180 Hz and 360 Hz. A pipe of length 0.75 m resonates at 300 Hz and 500 Hz but shows no resonance at 400 Hz.
(i) Identify the type of the pipe (open at both ends or closed at one end) and determine its fundamental frequency.
(ii) State the harmonic numbers corresponding to the pipe resonances at 300 Hz and 500 Hz.
(iii) Calculate the speed of sound in air using the pipe data.
(iv) When the third harmonic of the string and the higher of the two pipe resonances are sounded together, determine the beat frequency heard.
a. Identify the pipe type and its fundamental frequency.
b. Assign harmonic numbers to 300 Hz and 500 Hz.
c. Compute the speed of sound in air.
d. Find the beat frequency between the specified notes.