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Tcecarenko [31]

2 years ago

15

The human ear canal is, on average, 2.5cm long and aids in hearing by acting like a resonant cavity that is closed on one end an

d open on the other. The length of the ear canal is partially responsible for our sensitivities to certain frequencies. Use 340m/s for the speed of sound when performing the following calculations. What is the first resonant frequency?

1 answer:

Troyanec [42]2 years ago

4 0

Answer:

$3400$ Hz

Explanation:

We know that

1 cm = 0.01 m

$L$ = Length of the human ear canal = 2.5 cm = 0.025 m

$V$ = Speed of sound = 340 ms⁻¹

$f$ = First resonant frequency

The human ear canal behaves as a closed pipe and for a closed pipe, nth resonant frequency is given as

$f = \frac{(2n - 1)V}{4L}$

for first resonant frequency, we have n = 1

Inserting the values

$f = \frac{(2(1) - 1) 340}{4(0.025)}$

$f = \frac{340}{4(0.025)}$

$f = 3400$ Hz

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Explanation:

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(a ) In a motion on circular path , work done is zero because force ( centripetal force ) acts perpendicular to displacement .

( b )

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Putting the values

60 = .072 x ω² x 0.9

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Explanation:

1)

The period of a simple pendulum is given by

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The angular acceleration of the rotating disc is given by the equation

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$\omega_i$ is the initial angular velocity

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For a simple harmonic oscillator, the acceleration and the displacement of the system are related by the equation

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which implies that

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Therefore, the frequency of this simple harmonic oscillator is

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When the mass is hanging on the sping, the weight of the mass is equal to the restoring force on the spring, so we can write

$mg=kx$

where

m is the mass

$g=9.8 m/s^2$ is the acceleration of gravity

k is the spring constant

x = 8.0 cm = 0.08 m is the stretching of the spring

We can re-arrange the equation as

$\frac{k}{m}=\frac{g}{x}=\frac{9.8}{0.08}=122.5$

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According to the equation of continuity, the volume flow rate must remain constant, so we can write

$A_1 v_1 = A_2 v_2$

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$A_2 = \pi r_2^2$ is the area of the bigger piston, with $r_2= 15 cm$ being its radius

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Learn more about pressure:

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Answer:

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