A car's rear parking-sensor unit emits a train of ultrasonic sound pulses to detect obstacles behind the vehicle. The sensor operates at a frequency of 40 kHz, and sound travels through the air at 340 m/s. Calculate the wavelength of the ultrasonic pulses, giving your answer in…

Answer: C. Step 1: Recall the wave equation Wave speed, frequency and wavelength are linked by: v = f Rearranging for wavelength: = v/f Step 2: Convert the frequency into hertz The sensor's frequency is given in kilohertz, so it must be converted to…

IGCSE Physics 0625: Wavelength of an Ultrasonic Parking-Sensor Pulse

Step 1: Recall the wave equation

Wave speed, frequency and wavelength are linked by:

$v = f\lambda$

Rearranging for wavelength:

$\lambda = \frac{v}{f}$

Step 2: Convert the frequency into hertz

The sensor’s frequency is given in kilohertz, so it must be converted to hertz before it can be substituted into the formula:

$f = 40\text{ kHz} = 40\,000\text{ Hz}$

Step 3: Substitute the values

$\lambda = \frac{340\text{ m/s}}{40\,000\text{ Hz}}$

$\lambda = 0.0085\text{ m}$

Step 4: Convert into millimetres

$0.0085\text{ m} \times 1000 = 8.5\text{ mm}$

$\lambda = 8.5\text{ mm}$

Why the other options are wrong

Option	How it arises	Error
$8.5\text{ m}$	$340 \div 40$	Forgot to convert $40\text{ kHz}$ into $40\,000\text{ Hz}$ before dividing
$118\text{ mm}$	$40\,000 \div 340$	Formula inverted ( $f \div v$ instead of $v \div f$ )
$0.0085\text{ mm}$	$340 \div 40\,000\,000$	Extra factor-of-1000 slip when converting metres to millimetres

Final answers

Wavelength of the ultrasonic pulses $= \boxed{8.5\text{ mm}}$ , option C