An organ pipe is 248 cm long.(a) determine the fundamental overtone if the pipe is closed at one end.(b) determine the first audible overtone if the pipe is closed at one end.(c) determine the second audible overtone if the pipe is closed at one end.(d) determine the third audible overtone if the pipe is closed at one end.(e) determine the fundamental overtone if the pipe is open at both ends.(f) determine the first audible overtone if the pipe is open at both ends.(g) determine the second audible overtone if the pipe is open at both ends.(h) determine the third audible overtone if the pipe is open at both end.

(a) 34.6 Hz

The fundamental frequency of a pipe closed at one end is given by

where

v = 343 m/s is the speed of the sound in air

L is the length of the pipe

In this problem,

L = 248 cm = 2.48 m

So, the fundamental frequency is

(b) 103.8 Hz

In a open-closed pipe, only odd harmonics are produced; therefore, the frequency of the first overtone (second harmonic) is given by:

where

is the fundamental frequency.

Substituting into the equation,

(c) 173 Hz

The frequency of the second overtone (third harmonic) is given by:

where

is the fundamental frequency.

Substituting into the equation,

(d) 242.2 Hz

The frequency of the third overtone (fourth harmonic) is given by:

where

is the fundamental frequency.

Substituting into the equation,

(e) 69.2 Hz

The fundamental frequency of a pipe open at both ends is given by

where

v = 343 m/s is the speed of the sound in air

L is the length of the pipe

In this problem,

L = 248 cm = 2.48 m

So, the fundamental frequency is

(f) 138.4 Hz

In a open-open pipe, both odd and even harmonics are produced; therefore, the frequency of the first overtone (second harmonic) is given by:

where

is the fundamental frequency.

Substituting into the equation,

(g) 207.6 Hz

The frequency of the second overtone (third harmonic) in an open-open pipe is given by:

where

is the fundamental frequency.

Substituting into the equation,

(h) 276.8 Hz

The frequency of the third overtone (fourth harmonic) in an open-open pipe is given by:

where

is the fundamental frequency.

Substituting into the equation,

the only real purpose of sputnik 1 was to beat the us into space. we were getting close to launching a useful satellite, explorer 1 - which launched on january 31, 1958. the ussr had to beat that, so they launched sputnik 1 on october 4, 19

the old price per ounce is c/4.

the new price per ounce is c/3.6.

the ratio of the old price to the new one is

(c/4)/(c/3.6) = (c/c)×(3.6/4) = 0.9 . . = 9/10 . . "nine tenths" in either form