problem 1. You notice that a string fixed at both ends produces standing waves at 440...

problem 1. You notice that a string fixed at both ends produces standing waves at 440 Hz and 660 Hz, but not at any frequency in between.

a.What harmonics do these two frequencies correspond to?

b. What is the fundamental frequency?

problem 2. A bass clarinet can be modeled as a 120-cm-long tube closed at one end. A musician starts playing at room temperature (vsound = 343 m/s), but the temperature soon increases to where the speed of sound is 352 m/s. What is the change in the fundamental frequency?

problem 3. Three successive resonance frequencies in an organ pipe are 1310, 1834, and 2358 Hz. What is the length of the pipe?

Solutions

Expert Solution

1. 440 hz and 660 Hz, are multiples of 220 Hz,

The string will vibrate in harmonics of its fundamental frequency. The string vibrates in 2nd (2*220) and 3rd (220*3) harmonic.

Fundamental frequency is 220 Hz.

2. length of the tube = 120 cm long

at fundamental frequency the closed end of tube will have anode and the open end an anti-node.

L = /4 = 120 cm

= 4.8 m

sound speed at room temp = 343 m/s

at higher temp speed = 352 m/s

frequency f = v/

change in frequency = (352-343)/4.8 = 1.875 hz.

3) successive frequencies - 1310,1834, 2358

difference between the frequencies = 524 Hz,

These are multiples of 262 , - fundamental frequency

It is closed pipe and produces only odd harmonics , 1,3,5,7, 9

The frequencies produced are 5th, 7th and 9th harmonics

at fundamental frequency L = /4 =v/4f = (343/262)*1/4 = 0.327 m

genius_generous answered 1 month ago

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