Question

The motion detector used in a physics lab sends and receives 45 kHz ultrasonic pulses. A pulse goes out, reflects off the object being measured, and returns to the detector. The lab temperature is 20 ∘C.

What is the wavelength of the waves emitted by the motion detector?

Answer 1

The wavelength of the waves emitted by the motion detector with a frequency of 45 kHz in a 20°C lab is 7.62 mm, calculated using the speed of sound in air at that temperature and the wavelength formula (λ = speed of sound / frequency).

Step-by-step explanation:

To find the wavelength of the waves emitted by the motion detector at a frequency of 45 kHz in a lab at 20°C, we can use the formula for the speed of sound in air at a given temperature to first find the speed of sound and then use the wavelength formula.

The speed of sound at 20°C is approximately 343 m/s. Then the wavelength (λ) can be calculated using the wave formula:

λ = v / f

Where λ is the wavelength, v is the speed of sound (343 m/s), and f is the frequency (45 kHz).

λ = 343 m/s / 45×1000 Hz

λ = 0.00762 meters or 7.62 mm

So, the wavelength of the waves emitted by the motion detector is 7.62 mm.