If the intensity level of one trombone is 70 dB, calculate a reasonable estimate for the intensity level of 76 trombones all pla
1 answer:
Answer:
β₂ = 88.8 dβ
Explanation:
The intensity of the sound is
β = 10 log (I / I₀)
The sensitivity threshold (I₀) for humans is 1 10⁻¹² W / m²
I = I₀
I = 10⁻¹² 10^{70/10}
I = 1 10⁻⁵ W / m²
The total intensity for the 76 trombones is
I_total = n I
I_total = 76 1 10⁻⁵
I_total = 76 10⁻⁵ W / m²
Let's find the sound level
β₂ = 10 log (76 10⁻⁵ / 10⁻¹²)
β₂ = 88.8 dβ
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Answer:
a) about 20.4 meters high
b) about 4.08 seconds
Explanation:
Part a)
To find the maximum height the ball reaches under the action of gravity (g = 9.8 m/s^2) use the equation that connects change in velocity over time with acceleration.
In our case, the initial velocity of the ball as it leaves the hands of the person is Vi = 20 m/s, while thw final velocity of the ball as it reaches its maximum height is zero (0) m/s. Therefore we can solve for the time it takes the ball to reach the top:
Now we use this time in the expression for the distance covered (final position Xf minus initial position Xi) under acceleration:
Part b) Now we use the expression for distance covered under acceleration to find the time it takes for the ball to leave the person's hand and come back to it (notice that Xf-Xi in this case will be zero - same final and initial position)
To solve for "t" in this quadratic equation, we can factor it out as shown:
Therefore there are two possible solutions when each of the two factors equals zero:
1) t= 0 (which is not representative of our case) , and
2) the expression in parenthesis is zero: