Please Help. Thank you. I will Rate! Find the fundamental frequency and the freq
ID: 1382408 • Letter: P
Question
Please Help. Thank you. I will Rate!
Find the fundamental frequency and the frequency of the first three overtones of a pipe 75.0cm long, if the pipe is open at both ends. Please enter your answer as four numbers, separated with commas. Find the fundamental frequency and the frequency of the first three overtones of a pipe 75.0cm long, if the pipe is closed at one end. Please enter your answer as four numbers, separated with commas. If the pipe is open at both ends, what is the number of the highest harmonic that may be heard by a person who can hear frequencies from 20.0Hz to 2.00x104Hz ? If the pipe is closed at one end, what is the number of the highest harmonic that may be heard by a person who can hear frequencies from 20.0Hz to 2.00x104Hz ?Explanation / Answer
Take speed of sound, v = 340 m/s
A)
for a pipe open at both ends,
f_fund = v/(2*L)
= 340/(2*0.75)
= 226.67 Hz
f_ov1 = 2*226.67
= 453.3 Hz
f_ov2 = 3*226.67
= 680.01 Hz
f_ov3 = 4*226.67
= 906.68 Hz
B)
for a pipe open at one end,
f_fund = v/(4*L)
= 340/(4*0.75)
= 113.3 Hz
f_ov1 = 3*113.3
= 340 Hz
f_ov2 = 5*113.3
= 566.5 Hz
f_ov3 = 7*113.3
= 793.1 Hz
C) for an open pipe
f_max = n*f_fund (here n is even number)
n = f_max/f_fund
= 2*10^4/226.67
= 88
so, f_max = 88*226.67
= 19947 Hz
D) for a closed pipe
f_max = n*f_fund (here n is odd number)
n = f_max/f_fund
= 2*10^4/113.3
= 176.5
so, n = 175 (nearest odd number)
so, f_max = 175*113.3
= 19827 Hz