On a hot summer day (30 degrees Celcius), a pesky little mosquito produced its warning sound near your ear. The sound is produced by the beating of its wings at a rate of about 600 wing beats per second. What is the frequency in Hertz of the sound wave? What is the wavelength of the wave?

To determine the frequency of the mosquito's wing beats, we need to convert the given beats per second into Hertz (Hz). The frequency is defined as the number of cycles (or complete waveforms) per second.

1. Convert beats per second to Hertz:
Since 1 Hz is equal to 1 cycle per second, we can directly convert 600 beats per second to Hertz. Therefore, the frequency of the mosquito's wing beats is 600 Hz.

Next, let's determine the wavelength of the sound wave produced by the mosquito.

2. Calculate the wavelength of the wave:
The speed of sound in air can be approximated as 343 meters per second at room temperature. However, it is worth noting that the speed of sound can vary with temperature and humidity.

The formula to calculate the wavelength of a wave is:
Wavelength (λ) = Speed of sound (v) / Frequency (f)

In this case, we assume the speed of sound remains constant despite the temperature. Therefore, we can use the value of 343 meters per second.

Substituting the values into the formula:
Wavelength (λ) = 343 m/s / 600 Hz
Wavelength (λ) ≈ 0.572 meters (or 57.2 cm)

Therefore, the frequency of the mosquito's wing beats is 600 Hz, and the wavelength of the sound wave is approximately 0.572 meters (or 57.2 cm).

f=600 Hz,

speed of sound at 30 ºC v= 348,9 m/s
λ = v/f= 348.9/600= 0.58 m.

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