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2 years ago

A tuba creates a 4th harmonic of

Physics

1 answer:

nikklg [1K]2 years ago

6 0

Answer:

92.33Hz

Explanation:

A tuba is considered as having one open end and the other end is closed. Then:

f_n = n×v / 4L

so here

Where n = 4

f_4 = 116.5 Hz

116.5 Hz = nv/4L

116.5 Hz = 4v/4L

4×v / 4L = v / L

116.5 Hz = v/L............1

Let's assume the speed of sound is 343 m/s. Then substituting 343 m/s for v in equation 1

116.5 Hz = v/L

116.5 Hz = 343 m/s/L

Making L the subject

116.5 Hz × L = 343 m/s

L = 343m/s / 116.5Hz

= 2.944 m

Add 0.721 m to the length, and

f_4 = 343m/s / (2.944+0.721)m

f_4 = 343m/s ÷ 3.715

= 92.328 Hz

Approximately = 92.33Hz

Hence the new frequency for the 4th harmonic is 92.33Hz

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3 years ago

A bowling ball with a momentum of 18kg-m/s strikes a stationary bowling pin. After the collision, the ball has a momentum of 13k

Veronika [31]

Answer:

$14.98\ \text{kg m/s}$

$45.26^{\circ}$

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$P_1$ = Initial momentum of the pin = 13 kg m/s

$P_i$ = Initial momentum of the ball = 18 kg m/s

$P_2$ = Momentum of the ball after hit

$55^{\circ}$ = Angle ball makes with the horizontal after hitting the pin

$\theta$ = Angle the pin makes with the horizotal after getting hit by the ball

Momentum in the x direction

$P_i=P_1\cos55^{\circ}+P_2\cos\theta\\\Rightarrow P_2\cos\theta=P_i-P_1\cos55^{\circ}\\\Rightarrow P_2\cos\theta=18-13\cos55^{\circ}\\\Rightarrow P_2\cos\theta=10.54\ \text{kg m/s}$

Momentum in the y direction

$P_1\sin55=P_2\sin\theta\\\Rightarrow P_2\sin\theta=13\sin55^{\circ}\\\Rightarrow P_2\sin\theta=10.64\ \text{kg m/s}$

$(P_2\cos\theta)^2+(P_2\sin\theta)^2=P_2^2\\\Rightarrow P_2=\sqrt{10.54^2+10.64^2}\\\Rightarrow P_2=14.98\ \text{kg m/s}$

The pin's resultant velocity is $14.98\ \text{kg m/s}$

$P_2\sin\theta=10.64\\\Rightarrow \theta=sin^{-1}\dfrac{10.64}{14.98}\\\Rightarrow \theta=45.26^{\circ}$

The pin's resultant direction is $45.26^{\circ}$ below the horizontal or to the right.

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2 years ago