Aflutist assembles her flute in a room where the speed of sound is 342m/s . when she plays the note a, it is in perfect tune with a 440hz tuning fork. after a few minutes, the air inside her flute has warmed to where the speed of sound is 345m/s .

1.how many beats per second will she hear if she now plays the note a as the tuning fork is sounded?
2.how far does she need to extend the "tuning joint" of her flute to be in tune with the tuning fork?

a.3Hz

b.0.0034m

Explanation:

First, we know the flute is an open pipe, because open pipe as both end open and a close organ pipe as only one end close.

The formula relating the length and he frequency is giving as

.

a.we first determine the length of the flute at the fundamental frequency i.e when n=1 and when the speed is in the 342m/s

Hence from

.

since the value of the length will remain constant, we now use the value to determine the frequency when the air becomes hotter and the speed becomes 345m/s.

Hence the require beat is

.

b. since the length is dependent also on the speed and frequency, we determine the new length when she plays with a fundamental frequency when the speed of sound is 345m/s

using the formula

Now to determine the extension,