Part A $-$ Pattern $($a$)$ and Pattern $($b$)$: what are their wavelengths?

Learning Goal:

Standing Waves in a pipe that is open at one end but closed at the other end

The physics of wind instruments is based on the concept of standing waves. When the player blows into the mouthpiece, the column of air inside the instrument vibrates, and standing waves are produced. Althotigh the acoustics of wind instruments is complicated, a simple description in terms of open and closed tubes can help in understanding the physical phenomena related to these instruments.

For example, a clarinet can be described as an openclosed pipe because the mouthpiece of the clarinet is almost completely closed by the reed.

This figure shows $4$ standing wave patterns in an openclosed pipe. The length of the entire pipe is $L=1\mathrm{.}80m.$ The speed of sound in air is $v=343.\frac{m}{s}.$

Enter wavelength of pattern $($a$)$ first, followed by that of pattern $($b$),$ separate the two answers with a comma.

Keep $3$ digits after the decimal point, in meters

Pattern $($a$),($b$){}_a,{}_b=$

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Part B $-$ Pattern $($a$)$ and Pattern $($b$)$: what are their frequencies?

Enter frequency of pattern $($a$)$ first, followed by that of pattern $($b$),$ separate the two answers with a comm

Keep $2$ digits after the decimal point, in Hz

Pattern $($a$),($b$)f_a,f_b=$

$$ Hz

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Part C $-$ Pattern $($c$)$ and Pattern $($d$)$: what are their wavelengths?

Enter wavelength of pattern $($c$)$ first, followed by that of pattern $($d$),$ separate the two answers with a comma.

Keep $3$ digits after the decimal point, in meters