Lengths of a bass string

Question

An oboe and a double bass are playing the same note, a 'G' at 392 Hz. The speed of sound in air is 343 m s^-1 and the speed of propagation of a wave on the string of the double bass is 500 m s^-1. The oboe can be modeled as a pipe, open at one end, and the bass as a string fixed at both ends.

a) What are the lengths of the bass string and the oboe cavity if the note being produced is a result of the fundamental mode in each case?

Answer 1

1- For the oboe

f1=Vsound in air/ 4L

Use the first equation to find for the length of oboe cavity L

answer should be 0.218 m=21.8 cm

or you can find the wave length λ by dividing speed of sound over the frequency

λ= Vsound/ f

then divide λ by 4 to the length of the oboe cavity L

2- For the bass

f1= V of sound in the string /2L

Use the above equation to find L for the bass string length

L =V of sound in the string / 2 f1

L should be =0.637 m = 63.7 cm

or you can find λ then divide λ by 2 according to the first equation