Question

[5] 4. (a) Write a brief essay on standing waves on stringed musical instruments as compared to standing waves on the pipes of a pipe organ having pipes that are open at both ends as well as pipes that are open at one end and closed at the other. (b) You have been asked to determine the length of a metal tube that has been bent into a complex shape. One end of the tube is closed, the other end is open. Rather than doing something obvious and easy, like filling the tube with water, and then pouring it out and measuring the volume of water used; or poking a long wire down until it hits the end of the tube and then measuring the length of wire used; you decide to measure the standing wave frequencies of sound in the tube. You set up a speaker and a receiver at the open end of the tube, and start increasing the frequency from 1000 Hz. The first two resonances you find are at 1214 Hz and 1561 Hz. What is the length of the tube? (Take the speed of sound to be 343 m/s.) [5]

Please give detailed explanations/solutions, thank you!

Answer 1

1.Organ Pipe-Organ pipes are musical instrument which are used for producing musical sound by blowing air into the pipe.Longitudinal stationary waves are formed on account of superimposition of incident and reflected longitudinal waves.

​​​​​​Both end open-In open organ pipe all harmonics are present.

General formula-

X=2L/N

One end closed- It gives only odd harmonics.

General formula-
X= 4L/2N - 1

Stringed musical instruments have string fixed at both ends.In both end fixed string frequency can be represented by​​​​The string player changes the note by changing the effective length.Instrument emit multiple harmonics with different strengths which gives the instrument a unique sound.

V = nu/2L

2.

(5) И y = 2 - 1 Vtor у з 12 1ч 12 С , Е 1 С6 ( Иг 12ч = 343 k 161 3х33 = = 0. 02 m B ( = 0,16 м 49. че