Please can anyone explain. Thank you.
A rocket is launched vertically from ground with a constant acceleration. If the rocket emits a burst of sound every five seconds after launching, find the difference of intensity levels observed at the launching site for the first and the second bursts of sound.
To answer this question, we need to understand the concept of intensity levels and how they change with respect to distance.
Intensity level is a measure of the power per unit area carried by a sound wave. It is typically measured in decibels (dB). The formula to calculate intensity level (L) is given by:
L = 10 * log10(I / I0)
Where:
L is the intensity level in decibels,
I is the intensity of the sound wave, and
I0 is the reference intensity level which is usually set at 10^-12 Watts/m^2.
In this case, the rocket emits a burst of sound every five seconds after launching. As the rocket moves vertically upwards, the distance between the source of the sound (rocket) and the observer (launching site) increases. This results in a decrease in the intensity of the sound wave due to the spreading out of the sound energy over a larger area.
To find the difference in intensity levels observed at the launching site for the first and second bursts of sound, we need to consider the change in distance between the observer and the rocket for each burst.
Let's assume that at the time of the first burst of sound, the rocket is at a height 'h1' above the ground. Similarly, at the time of the second burst of sound, the rocket is at a height 'h2' above the ground. The difference in height between the two bursts is given by 'Δh = h2 - h1'.
To calculate the difference in intensity levels observed, we can use the inverse square law for sound propagation, which states that the intensity of a sound wave is inversely proportional to the square of the distance from the source.
Let's assume that the intensity of the sound wave at the launching site for the first burst is 'I1' and for the second burst is 'I2'. The relationship between the two intensities can be expressed as:
I2 = I1 * (r1 / r2)^2
Where:
r1 is the initial distance between the rocket and the launching site (h1),
r2 is the final distance between the rocket and the launching site (h2).
To find the difference in intensity levels observed, we can substitute the values into the formula for intensity level:
ΔL = 10 * log10(I2 / I0) - 10 * log10(I1 / I0)
Simplifying the formula, we get:
ΔL = 10 * log10((I1 * (r1 / r2)^2) / I0) - 10 * log10(I1 / I0)
= 10 * log10((r1 / r2)^2)
Finally, the difference in intensity levels observed at the launching site for the first and second bursts of sound can be calculated using the equation above, substituting the values of 'r1' and 'r2' in terms of 'h1' and 'h2'.
I hope this explanation helps you understand how to approach and solve this problem. If you have specific values for 'h1' and 'h2', you can substitute them into the equation to calculate the difference in intensity levels.
v=at so velocity is increasing linearly. So at time 1, v=5a, distance=v*t=25a
at time 2, v=10a, and distance=100a
so the distance is 4x as far, so the sound diminished as the square of the diatnace, so intensity is 1/16..