A standing wave pattern is created on a string with mass density $=3\mathrm{.}310-4$ kg$/$m$.$ A wave generator with frequency f $=67$ Hz is attached to one end of the string and the other end goes over a pulley and is connected to a mass $($ignore the weight of the string between the pulley and mass$).$ The distance between the generator and pulley is L $=0\mathrm{.}7$ m$.$ Initially the $3$rd harmonic wave pattern is formed.

$1)$

What is the wavelength of the wave?

m

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$2)$

What is the speed of the wave?

m$/$s

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$3)$

What is the tension in the string?

N

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$4)$

What is the mass hanging on the end of the string?

kg

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$5)$

Now the hanging mass is adjusted to create the $2$nd harmonic. The frequency is held fixed at f $=67$ Hz$.$

What is the wavelength of the wave?

m

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$6)$

What is the speed of the wave?

m$/$s

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$7)$

What is the tension in the string?

N

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$8)$

What is the mass hanging on the end of the string?

kg

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$9)$

Keeping the frequency fixed at f $=67$ Hz$,$ what is the maximum mass that can be used to still create a coherent standing wave pattern?

kg

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