A siren has 1000 holes, rotates with a rate of 200 rpm. What is the frequency of the sound emerging from it?

To determine the frequency of the sound produced by a siren with 1000 holes rotating at 200 revolutions per minute (rpm), we can break down the problem into manageable steps. The key here is to understand how the rotation of the siren and the number of holes contribute to the sound frequency.

Understanding the Basics

First, let's clarify what we mean by frequency. Frequency refers to the number of cycles or occurrences of a repeating event per unit of time, typically measured in Hertz (Hz), where 1 Hz equals one cycle per second.

Calculating the Frequency

In this scenario, the siren has 1000 holes, and it completes 200 revolutions every minute. To find the frequency of the sound, we need to calculate how many times each hole contributes to the sound in one second.

• Convert the revolutions per minute to revolutions per second:

Since there are 60 seconds in a minute, we can convert 200 rpm to revolutions per second (rps) as follows:

200 rpm ÷ 60 seconds/minute = 3.33 rps (approximately)

• Next, calculate the total number of holes passing a point in one second:

Since each revolution allows all 1000 holes to pass a point, we multiply the number of revolutions per second by the number of holes:

3.33 rps × 1000 holes = 3333 holes per second

Final Frequency Calculation

Now, we have determined that the siren produces 3333 cycles (or sound pulses) per second. Therefore, the frequency of the sound emerging from the siren is:

Frequency = 3333 Hz

Summary of the Process

To summarize, we calculated the frequency of the sound from the siren by first converting the rotation speed from revolutions per minute to revolutions per second. Then, we multiplied the number of revolutions per second by the number of holes to find the total sound frequency. This method illustrates how mechanical movement can translate into sound waves, showcasing the fascinating relationship between physics and acoustics.