Questionwledge A mosquito beats its wings at a rate of about 6,000 wing beats per minute. a. What is the frequency in Hertz of the sound wave created by the mosquito's wings? b. Assuming the sound wave moves with a velocity of $350 \mathrm{~m} / \mathrm{s}$ , what is the wavelength of $t$ [4] sound wave generated by the beating wings?

Studdy Solution

STEP 1

1. A mosquito beats its wings at a rate of 6,000 wing beats per minute.
2. Frequency is measured in Hertz (Hz), which is equivalent to cycles per second.
3. The velocity of the sound wave is given as $350 \, \text{m/s}$ .
4. We need to find the frequency in Hertz and the wavelength of the sound wave.

STEP 2

1. Convert wing beats per minute to frequency in Hertz.
2. Calculate the wavelength using the frequency and velocity of the sound wave.

STEP 3

Convert wing beats per minute to frequency in Hertz.
To convert beats per minute to Hertz, divide by 60 (since there are 60 seconds in a minute):
$\text{Frequency (Hz)} = \frac{6000 \, \text{beats/minute}}{60 \, \text{seconds/minute}}$
$\text{Frequency (Hz)} = 100 \, \text{Hz}$

STEP 4

Calculate the wavelength using the frequency and velocity of the sound wave.
The relationship between velocity ( $v$ ), frequency ( $f$ ), and wavelength ( $\lambda$ ) is given by the equation:
$v = f \times \lambda$
Rearrange the equation to solve for wavelength ( $\lambda$ ):
$\lambda = \frac{v}{f}$
Substitute the given values:
$\lambda = \frac{350 \, \text{m/s}}{100 \, \text{Hz}}$
$\lambda = 3.5 \, \text{m}$
The frequency of the sound wave is $100 \, \text{Hz}$ and the wavelength is $3.5 \, \text{m}$ .

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